To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)pre...To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.展开更多
This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaoti...This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.展开更多
Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields,including cryptography,optics,and secure communications.In this p...Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields,including cryptography,optics,and secure communications.In this paper,a three-dimensional fractional-order chaotic Lorenz model of chemical reactions is discussed.Some basic dynamical properties,such as stability of equilibria,Lyapunov exponents,bifurcation diagrams,Poincarémap,and sensitivity to initial conditions,are studied.By adopting the Adomian decomposition algorithm(ADM),the numerical solution of the fractional-order system is obtained.It is found that the lowest derivative order in which the proposed system exhibits chaos is q=0.694 by applying ADM.The result has been validated by the existence of one positive Lyapunov exponent and by employing some phase diagrams.In addition,the richer dynamics of the system are confirmed by using powerful tools in nonlinear dynamic analysis,such as the 0-1 test and C_(0)complexity.Moreover,modified projective synchronization has been implemented based on the stability theory of fractional-order systems.This paper presents the application of the modified projective synchronization in secure communication,where the information signal can be transmitted and recovered successfully through the channel.MATLAB simulations are provided to show the validity of the constructed secure communication scheme.展开更多
This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays.Since the introduction of memristor,the presented models are nonlinear systems with chaotic dynamics.First,...This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays.Since the introduction of memristor,the presented models are nonlinear systems with chaotic dynamics.First,the TS fuzzy method is adopted to describe the chaotic systems.Then,a sliding-model-based control approach is proposed to achieve the preassigned-time stabilization of the presented models,where the upper bound of stabilization time can be arbitrarily specified in advance.Finally,simulation results demonstrate the validity of presented control approach and theoretic results.展开更多
Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is desi...Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper.While ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic keys.The highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark images.The experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works.展开更多
A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are con...A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.展开更多
Chaos is a type of motion unique to nonlinear dynamical systems,characterized by extreme sensitivity to initial conditions and the randomness,which makes it potentially useful for secure communication.Chaos research r...Chaos is a type of motion unique to nonlinear dynamical systems,characterized by extreme sensitivity to initial conditions and the randomness,which makes it potentially useful for secure communication.Chaos research require a easily controllable chaotic oscillator.Chaotic behavior in optical bistability provides a simple theoretical model.Based on the theoretical model,a novel chaotic oscillator in frequency domain is proposed.The chaotic oscillator is composed of a tunable fiber laser,fiber Fabry⁃Perot interferometer(FFPI)and hybrid delayed feedback loop.The laser itself plays a part in delay time which is induced by PZT device.The chaotic oscillator is realized by experiments and chaos behaviors are observed.The chaos oscillator has the characteristic of simplicity and flexibility.It have potential application value in the field of fiber optical communication encryption.展开更多
Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchroni...Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.展开更多
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide...This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.展开更多
This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process, eight different types of operations are used to encrypt the pixels o...This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and one of them will be used for particular pixels decided by the outcome of the chaotic map lattices. To make the cipher more robust against any attacks, the secret key is modified after encrypting each block of sixteen pixels of the image. The experimental results and security analysis show that the proposed image encryption scheme achieves high security and efficiency.展开更多
A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in stat...A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.展开更多
In this paper, an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the （2＋l）-dimensional Broek-Kaup equation with variable coefficients （VCBK）. Base...In this paper, an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the （2＋l）-dimensional Broek-Kaup equation with variable coefficients （VCBK）. Based on the derived solitary wave solution and using a known chaotic system, some novel chaotic solutions are investigated.展开更多
A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability ...A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.展开更多
In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive...In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.展开更多
The finding of the compound structure of a new four-scrolls chaotic system is reported, which is obtained by merging together two symmetrical attractors. And the two symmetrical attractors are generated only by adding...The finding of the compound structure of a new four-scrolls chaotic system is reported, which is obtained by merging together two symmetrical attractors. And the two symmetrical attractors are generated only by adding a constant gain to the original system. Also, the forming procedure of the new four-scrolls chaotic attractor is explored and the relation between the constant gain and the properties of the system is given.展开更多
This paper numerically investigates the effects of dispersion on optical fibre chaotic communication, and proposes a dispersion compensation scheme to improve the performance of optical fibre chaotic communication sys...This paper numerically investigates the effects of dispersion on optical fibre chaotic communication, and proposes a dispersion compensation scheme to improve the performance of optical fibre chaotic communication system. The obtained results show that the transmitter-receiver synchronization progressively degrades and the signal-to-noise ratio of the recovered message deteriorates as the fibre length increases due to the dispersion accumulation. Two segments of 2.5-km dispersion-compensating fibres are symmetrically placed at both ends of a segment of 245-km nonzero dispersionshifted fibre with low dispersion in one compensation period. The numerical results show that the signal-to-noise ratio of the extracted 1 GHz sinusoidal message is improved from -2.92 dB to 15.38 dB by this dispersion compensation for the transmission distance of 500 km.展开更多
A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can gener...A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.展开更多
This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a syn...This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
The algorithm is an image encryption algorithm based on the improved baker transformation and chaotic substitution box(S-box). It mainly uses the initial values and parameters of a one-dimensional logistic chaotic sys...The algorithm is an image encryption algorithm based on the improved baker transformation and chaotic substitution box(S-box). It mainly uses the initial values and parameters of a one-dimensional logistic chaotic system as an encryption key. Specifically, in the image scrambling stage, the algorithm primarily uses an improved baker transform method to process the image. In the image diffusion stage, the algorithm first uses the chaotic S-box method to process the encryption key. Secondly, an exclusive OR(XOR) operation is performed on the image and the encryption key to initially diffuse the image. Finally, the image is again diffused using the method of ortho XOR. Simulation analysis shows that the algorithm can achieve good encryption effect, simple and easy implementation, and good security. In the digital image communication transmission, it has good practical value.展开更多
文摘To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.
基金Project supported by the Open Fund of Anhui Key Laboratory of Mine Intelligent Equipment and Technology (Grant No.ZKSYS202204)the Talent Introduction Fund of Anhui University of Science and Technology (Grant No.2021yjrc34)the Scientific Research Fund of Anhui Provincial Education Department (Grant No.KJ2020A0301)。
文摘This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities.
文摘Synchronization of fractional-order chaotic systems is receiving significant attention in the literature due to its applications in a variety of fields,including cryptography,optics,and secure communications.In this paper,a three-dimensional fractional-order chaotic Lorenz model of chemical reactions is discussed.Some basic dynamical properties,such as stability of equilibria,Lyapunov exponents,bifurcation diagrams,Poincarémap,and sensitivity to initial conditions,are studied.By adopting the Adomian decomposition algorithm(ADM),the numerical solution of the fractional-order system is obtained.It is found that the lowest derivative order in which the proposed system exhibits chaos is q=0.694 by applying ADM.The result has been validated by the existence of one positive Lyapunov exponent and by employing some phase diagrams.In addition,the richer dynamics of the system are confirmed by using powerful tools in nonlinear dynamic analysis,such as the 0-1 test and C_(0)complexity.Moreover,modified projective synchronization has been implemented based on the stability theory of fractional-order systems.This paper presents the application of the modified projective synchronization in secure communication,where the information signal can be transmitted and recovered successfully through the channel.MATLAB simulations are provided to show the validity of the constructed secure communication scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62473348 and 62076229)the Knowledge Innovation Program of Wuhan-Basic Research(Grant No.2023010201010101).
文摘This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays.Since the introduction of memristor,the presented models are nonlinear systems with chaotic dynamics.First,the TS fuzzy method is adopted to describe the chaotic systems.Then,a sliding-model-based control approach is proposed to achieve the preassigned-time stabilization of the presented models,where the upper bound of stabilization time can be arbitrarily specified in advance.Finally,simulation results demonstrate the validity of presented control approach and theoretic results.
基金Project supported by the National Natural Science Foundation of China(Grant No.62061014)the Natural Science Foundation of Liaoning province of China(Grant No.2020-MS-274).
文摘Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper.While ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic keys.The highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark images.The experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62105004 and 52174141)the College Student Innovation and Entrepreneurship Fund Project(Grant No.202210361053)+1 种基金Anhui Mining Machinery and Electrical Equipment Coordination Innovation Center,Anhui University of Science&Technology(Grant No.KSJD202304)the Anhui Province Digital Agricultural Engineering Technology Research Center Open Project(Grant No.AHSZNYGC-ZXKF021)。
文摘A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.
文摘Chaos is a type of motion unique to nonlinear dynamical systems,characterized by extreme sensitivity to initial conditions and the randomness,which makes it potentially useful for secure communication.Chaos research require a easily controllable chaotic oscillator.Chaotic behavior in optical bistability provides a simple theoretical model.Based on the theoretical model,a novel chaotic oscillator in frequency domain is proposed.The chaotic oscillator is composed of a tunable fiber laser,fiber Fabry⁃Perot interferometer(FFPI)and hybrid delayed feedback loop.The laser itself plays a part in delay time which is induced by PZT device.The chaotic oscillator is realized by experiments and chaos behaviors are observed.The chaos oscillator has the characteristic of simplicity and flexibility.It have potential application value in the field of fiber optical communication encryption.
基金supported by the Education Committee of Chongqing Province,China (Grant No.KJ090503)
文摘Based on the idea of tracking control and stability theory of fractional-order systems, a controller is designed to synchronize the fractional-order chaotic system with chaotic systems of integer orders, and synchronize the different fractional-order chaotic systems. The proposed synchronization approach in this paper shows that the synchronization between fractional-order chaotic systems and chaotic systems of integer orders can be achieved, and the synchronization between different fractional-order chaotic systems can also be realized. Numerical experiments show that the present method works very well.
基金Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin,China (Grant Nos 07JCZDJC09600,08JCZDJC21900 and 08JCZDJC18600)the Tianjin Key Laboratory for Control Theory & Applications in Complicated Industry Systems of China
文摘This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.
基金supported by the National Natural Science Foundation of China (Grant Nos. 61001099 and 10971120)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200444)
文摘This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices. In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and one of them will be used for particular pixels decided by the outcome of the chaotic map lattices. To make the cipher more robust against any attacks, the secret key is modified after encrypting each block of sixteen pixels of the image. The experimental results and security analysis show that the proposed image encryption scheme achieves high security and efficiency.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61201452)
文摘A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.
基金supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y6100257 and Y6090681)the Natural Science Foundation of Zhejiang Lishui University (Grant Nos. KZ09005 and KY08003)
文摘In this paper, an improved projective approach is used to obtain the variable separation solutions with two arbitrary functions of the （2＋l）-dimensional Broek-Kaup equation with variable coefficients （VCBK）. Based on the derived solitary wave solution and using a known chaotic system, some novel chaotic solutions are investigated.
基金Project supported by the National Natural Science Foundation of China （Grant No 20373021） and Natural Science Foundation of Liaoning Province （Grant No 20052151）.
文摘A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.
基金Project supported by the National Natural Science Foundation of China （Grant No 60574045） and partly by Foundation of Guangxi Department of Education, China （Grant No （2006）26-118）.
文摘In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
文摘The finding of the compound structure of a new four-scrolls chaotic system is reported, which is obtained by merging together two symmetrical attractors. And the two symmetrical attractors are generated only by adding a constant gain to the original system. Also, the forming procedure of the new four-scrolls chaotic attractor is explored and the relation between the constant gain and the properties of the system is given.
基金supported by the National Natural Science Foundation of China (Grant Nos 60777041 and 60577019)the International Cooperation Project of Shanxi Province,China (Grant No 2007081019)
文摘This paper numerically investigates the effects of dispersion on optical fibre chaotic communication, and proposes a dispersion compensation scheme to improve the performance of optical fibre chaotic communication system. The obtained results show that the transmitter-receiver synchronization progressively degrades and the signal-to-noise ratio of the recovered message deteriorates as the fibre length increases due to the dispersion accumulation. Two segments of 2.5-km dispersion-compensating fibres are symmetrically placed at both ends of a segment of 245-km nonzero dispersionshifted fibre with low dispersion in one compensation period. The numerical results show that the signal-to-noise ratio of the extracted 1 GHz sinusoidal message is improved from -2.92 dB to 15.38 dB by this dispersion compensation for the transmission distance of 500 km.
文摘A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.
文摘This paper investigates the synchronization between integer-order and fractional-order chaotic systems. By intro- ducing fractional-order operators into the controllers, the addressed problem is transformed into a synchronization one among integer-order systems. A novel general method is presented in the paper with rigorous proof. Based on this method, effective controllers are designed for the synchronization between Lorenz systems with an integer order and a fractional order, and for the synchronization between an integer-order Chen system and a fractional-order Liu system. Numerical results, which agree well with the theoretical analyses, are also given to show the effectiveness of this method.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
基金supported by the National Natural Science Foundation of China (Grant No. 61672124)the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund,China (Grant No. MMJJ20170203)+3 种基金the Liaoning Provincial Science and Technology Innovation Leading Talents Program Project,China (Grant No. XLYC1802013)the Key Research and Development Projects of Liaoning Province,China (Grant No. 2019020105-JH2/103)the Jinan City ‘20 universities’ Funding Projects Introducing Innovation Team Program,China (Grant No. 2019GXRC031)the “Double First-rate”Construction Project (“Innovation Project”),China (Grant No. SSCXXM013)。
文摘The algorithm is an image encryption algorithm based on the improved baker transformation and chaotic substitution box(S-box). It mainly uses the initial values and parameters of a one-dimensional logistic chaotic system as an encryption key. Specifically, in the image scrambling stage, the algorithm primarily uses an improved baker transform method to process the image. In the image diffusion stage, the algorithm first uses the chaotic S-box method to process the encryption key. Secondly, an exclusive OR(XOR) operation is performed on the image and the encryption key to initially diffuse the image. Finally, the image is again diffused using the method of ortho XOR. Simulation analysis shows that the algorithm can achieve good encryption effect, simple and easy implementation, and good security. In the digital image communication transmission, it has good practical value.
