A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conse...A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.展开更多
Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identi...Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.展开更多
We present a specific state variable for a class of fractional-order chaotic systems. By using a specific state variable and its （q-order, 2q-order, ..., and （n-1） q-order） time derivatives, all the state variable...We present a specific state variable for a class of fractional-order chaotic systems. By using a specific state variable and its （q-order, 2q-order, ..., and （n-1） q-order） time derivatives, all the state variables can be obtained. Several fractional-order chaotic systems are used to demonstrate this idea. A hybrid projective synchronization scheme is presented to show its applications.展开更多
We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization ...We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization via the open-plus-closed-loop control, which allows us to arbitrarily manipulate the scaling factor of projective synchronization. The proposed scheme is proved analytically on the basis of the stability theorem of the fractional differential equations. Numerical simulations on the fraction-order chaotic Chen system are presented to justify the theoretical analysis.展开更多
To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree...To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to theunderstanding of robustness of complex networks with reparability.展开更多
A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transforma...A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos.展开更多
Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity sli...Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity slip parameter resulting in an increase in the temperature field. The rate of heat transfer decreases with the velocity slip parameter while it increases with unsteadiness parameter. The same feature is also noticed for thermal slip parameter.展开更多
We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on t...We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.展开更多
The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from t...The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.展开更多
Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensio...Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.展开更多
A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） ...A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.展开更多
It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the ...It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the truncated Painlevé approach. Using the BT, the model is transformed to a system of equations, which finally leads to a special variable separation solution with arbitrary functions.展开更多
We study the features of a single q-breather （SQB） in a Fermi-Pasta-Ulam lattice by the numerical method, and obtain that the stability of SQB correlates to coupling constant K and nonlinear parameter β. No matter ...We study the features of a single q-breather （SQB） in a Fermi-Pasta-Ulam lattice by the numerical method, and obtain that the stability of SQB correlates to coupling constant K and nonlinear parameter β. No matter whether K or β increases, the periodic SQB can be transformed into a quasiperiodic SQB or a chaotic SQB. We also obtain the conditions of excitation of periodic, quasiperiodic and chaotic SQBs.展开更多
Recently, the cryptosystem based on chaos has attracted much attention. Wang and Yu （Commun. Nonlin. Sci. Numer. Simulat. 14（2009）574） proposed a block encryption algorithm based on dynamic sequences of multiple c...Recently, the cryptosystem based on chaos has attracted much attention. Wang and Yu （Commun. Nonlin. Sci. Numer. Simulat. 14（2009）574） proposed a block encryption algorithm based on dynamic sequences of multiple chaotic systems. We analyze the potential flaws in the algorithm. Then, a chosen-plaintext attack is presented. Some remedial measures are suggested to avoid the flaws effectively. Furthermore, an improved encryption algorithm is proposed to resist the attacks＂ and to keep all the merits of the original cryptosystem.展开更多
Recently, quantitative study on complex systems has become an attractive research area for physicists. Human scientific activity, including scientific paper publication, is an important complex system and therefore de...Recently, quantitative study on complex systems has become an attractive research area for physicists. Human scientific activity, including scientific paper publication, is an important complex system and therefore deserves an investigation. We present a simple model to describe the interaction between journals, authors and editorial board members. In the model the probabilities, with which a journal accepts papers from an author or invites him as an editorial board member, obey normal distributions. However, the most probable value of the latter distribution shifts such that the journal can have higher level authors being its editorial board members. The analytic derivation by the model is in rather good agreement with the empirical observation from the selected fifteen worldwide journals with different impact factors.展开更多
Synchronization behavior of coupled dynamical systems is discussed. An equivalence relation is found between the diffeomorphic generalized synchronization and the complete synchronization of coupled nonidentical syste...Synchronization behavior of coupled dynamical systems is discussed. An equivalence relation is found between the diffeomorphic generalized synchronization and the complete synchronization of coupled nonidentical systems. Employing the method of the complete synchronization, the problem of the generalized synchronization can be unraveled. By constructing an appropriate coupling term, a sufficient condition is obtained for determining the complete synchronization of coupled nonidentical systems. Numerical simulations are also given to show the effectiveness of the proposed schemes.展开更多
The problem of chaos control and complete synchronization of cellular neural network with delays is studied. Based on the open plus nonlinear closed loop （OPNCL） method, the control scheme and synchronization scheme...The problem of chaos control and complete synchronization of cellular neural network with delays is studied. Based on the open plus nonlinear closed loop （OPNCL） method, the control scheme and synchronization scheme are designed. Both the schemes can achieve the chaos control and complete synchronization of chaotic neural network respectively, and their validity is further verified by numerical simulation experiments.展开更多
We investigate how an initial thermo vacuum state, in the context of thermo field dynamics, evolves in a single-mode amplitude dissipative channel, and find that in this process the thermo squeezing effect decreases w...We investigate how an initial thermo vacuum state, in the context of thermo field dynamics, evolves in a single-mode amplitude dissipative channel, and find that in this process the thermo squeezing effect decreases while the fictitious-mode vacuum becomes chaotic.展开更多
文摘A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.
文摘Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.
文摘We present a specific state variable for a class of fractional-order chaotic systems. By using a specific state variable and its （q-order, 2q-order, ..., and （n-1） q-order） time derivatives, all the state variables can be obtained. Several fractional-order chaotic systems are used to demonstrate this idea. A hybrid projective synchronization scheme is presented to show its applications.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10871074 and 60704045, Research and for the Doctoral Program of Higher Education of China under Grant No 20070558053, and the Natural Science Foundation of Guangdong Province under Grant No 9451042001004076.
文摘We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization via the open-plus-closed-loop control, which allows us to arbitrarily manipulate the scaling factor of projective synchronization. The proposed scheme is proved analytically on the basis of the stability theorem of the fractional differential equations. Numerical simulations on the fraction-order chaotic Chen system are presented to justify the theoretical analysis.
文摘To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to theunderstanding of robustness of complex networks with reparability.
基金Supported by the National Natural Science Foundation of China under Grant No 10872141, and the National Basic Research Program of China under Grant No 2007CB714000.
文摘A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos.
文摘Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity slip parameter resulting in an increase in the temperature field. The rate of heat transfer decreases with the velocity slip parameter while it increases with unsteadiness parameter. The same feature is also noticed for thermal slip parameter.
文摘We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.
文摘The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.
基金Supported by the Graduate Student Creative Foundation of Hunan University of Science and Technology under Grant No S080111, Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry of China under Grant No 527[2004]） and the Hunan Provincial Natural Science Foundation under Grant No 06JJ2026.
文摘Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.
基金Supported by the National Natural Science Foundation of China under Grant No 10947138, and in part by the Research Foundation of Anhui Normal University under Grant No 2009xqn63.
文摘A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No 20070248120, SRF for ROCS, SEM, and the National Natural Science Foundation of China under Grant Nos 10735030 and 10905038.
文摘It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the truncated Painlevé approach. Using the BT, the model is transformed to a system of equations, which finally leads to a special variable separation solution with arbitrary functions.
基金Supported by the National Natural Science Foundation of China under Grant No 1057400, and the Natural Science Foundation of Heilongjiang Province under Grant No A200506.
文摘We study the features of a single q-breather （SQB） in a Fermi-Pasta-Ulam lattice by the numerical method, and obtain that the stability of SQB correlates to coupling constant K and nonlinear parameter β. No matter whether K or β increases, the periodic SQB can be transformed into a quasiperiodic SQB or a chaotic SQB. We also obtain the conditions of excitation of periodic, quasiperiodic and chaotic SQBs.
基金Supported by the National Natural Science Foundation of China under Grant No 61003256, the Natural Science Foundation of CQ CSTC （Nos 2009BB2282 and 2008BB2193）, the Doctor Foundation of Chongqing University of Posts and Telecommunications （A2009-01）, and the Foundation of Chongqing Key Laboratory of Electronic Commerce and Logistics （Nos ECML1003 and ECML1010）.
文摘Recently, the cryptosystem based on chaos has attracted much attention. Wang and Yu （Commun. Nonlin. Sci. Numer. Simulat. 14（2009）574） proposed a block encryption algorithm based on dynamic sequences of multiple chaotic systems. We analyze the potential flaws in the algorithm. Then, a chosen-plaintext attack is presented. Some remedial measures are suggested to avoid the flaws effectively. Furthermore, an improved encryption algorithm is proposed to resist the attacks＂ and to keep all the merits of the original cryptosystem.
基金Supported by the National Natural Science Foundation of China under grant Nos 10635040, 70671089 and 10705023.
文摘Recently, quantitative study on complex systems has become an attractive research area for physicists. Human scientific activity, including scientific paper publication, is an important complex system and therefore deserves an investigation. We present a simple model to describe the interaction between journals, authors and editorial board members. In the model the probabilities, with which a journal accepts papers from an author or invites him as an editorial board member, obey normal distributions. However, the most probable value of the latter distribution shifts such that the journal can have higher level authors being its editorial board members. The analytic derivation by the model is in rather good agreement with the empirical observation from the selected fifteen worldwide journals with different impact factors.
基金Supported by the National Science Foundation for Distinguished Young Scholars of China under Grant No 10425209, the National Natural Science Foundation of China under Grant No 10972011, the China Postdoctoral Science Foundation under Grant No 20080430295, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality.
文摘Synchronization behavior of coupled dynamical systems is discussed. An equivalence relation is found between the diffeomorphic generalized synchronization and the complete synchronization of coupled nonidentical systems. Employing the method of the complete synchronization, the problem of the generalized synchronization can be unraveled. By constructing an appropriate coupling term, a sufficient condition is obtained for determining the complete synchronization of coupled nonidentical systems. Numerical simulations are also given to show the effectiveness of the proposed schemes.
基金Supported by the National Natural Science Foundation of China under Nos 60973152 and 60573172, the Superior University Doctor Subject Special Scientific Research Foundation of China under Grant No 20070141014, and the Natural Science Foundation of Liaoning Province （No 20082165）.
文摘The problem of chaos control and complete synchronization of cellular neural network with delays is studied. Based on the open plus nonlinear closed loop （OPNCL） method, the control scheme and synchronization scheme are designed. Both the schemes can achieve the chaos control and complete synchronization of chaotic neural network respectively, and their validity is further verified by numerical simulation experiments.
文摘We investigate how an initial thermo vacuum state, in the context of thermo field dynamics, evolves in a single-mode amplitude dissipative channel, and find that in this process the thermo squeezing effect decreases while the fictitious-mode vacuum becomes chaotic.
