We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m...We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.展开更多
The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified resp...The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.展开更多
This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequal...This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.展开更多
The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statisti...The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.展开更多
Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic ...Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic dynamic modeling(SDM) is considered as an effective way to predict real-time satellite channel fading caused by rain. This article carries out a survey of SDM using stochastic differential equations(SDEs) currently in the literature. Special attention is given to the different input characteristics of each model to satisfy specific local conditions. Future research directions in SDM are also suggested in this paper.展开更多
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis ...Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.展开更多
In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail. Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are der...In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail. Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether＇s theorem.展开更多
Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions...Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions on the bilayer square lattice under a time varying （sinusoidal） magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic （FM/FM） and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.展开更多
In order to improve the transform efficiency of bi-stable energy harvester（BEH）,this paper proposes an advanced bi-stable energy harvester（ABEH）,which is composed of two bi-stable beams coupling through their magn...In order to improve the transform efficiency of bi-stable energy harvester（BEH）,this paper proposes an advanced bi-stable energy harvester（ABEH）,which is composed of two bi-stable beams coupling through their magnets.Theoretical analyzes and simulations for the ABEH are carried out.First,the mathematical model is established and its dynamical equations are derived.The formulas of magnetic force in two directions are given.The potential energy barrier of ABEH is reduced and the snap-through is liable to occur between potential wells.To demonstrate the ABEH＇s advantage in harvesting energy,comparisons between the ABEH and the BEH are carried out for both harmonic and stochastic excitations.Our results reveal that the ABEH＇s inter-well response can be elicited by a low-frequency excitation and the harvester can attain frequent jumping between potential wells at fairly weak random excitations.Thus,it can generate a higher output power.The present findings prove that the ABEH is preferable in harvesting energy and can be optimally designed such that it attains the best harvesting performance.展开更多
The highly excited vibrational levels of HCO in the electronic ground state, X^1A＇, are employed to determine the coefficients of an algebraic Hamiltonian, by which the dynamical potential is derived and shown to be ...The highly excited vibrational levels of HCO in the electronic ground state, X^1A＇, are employed to determine the coefficients of an algebraic Hamiltonian, by which the dynamical potential is derived and shown to be very useful for interpreting the intramolecular vibrational relaxation （IVR） which operates via the HCO bending motion. The IVR inhibits the dissociation of H atom and enhances the stochastic degree of dynamical character. This approach is from a global viewpoint on a series of levels classified by the polyad number which is a constant of motion in a certain dynamical domain. In this way, the seemingly complicated level structure shows very regular picture, dynamically.展开更多
Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the ...Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named ＂the equation of life＂. Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerfu! Boltzmann-Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology.展开更多
The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system...The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glauber- type stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions （first- or second-order） is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic （P）, antiferromagnetic （AF5/2, AF3/2, AF1/2） phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.展开更多
基金Project supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20220917)the National Natural Science Foundation of China (Grant Nos.12001213 and 12302035)。
文摘We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon＇s information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
基金Project supported by the National Natural Science Foundation of China (Grant No.11002061)
文摘The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.
基金supported by the National Natural Science Foundation of China (Grant No.60974139)the Fundamental Research Funds for the Central Universities (Grant No.72103676)
文摘This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.
基金Project supported by the National Natural Science Foundation for Distinguished Young Scholars of China(Grant No.11125419)the National Natural Science Foundation of China(Grant No.10925525)+1 种基金the Funds for the Leading Talents of Fujian ProvinceChina
文摘The Langevin approach has been applied to model the random open and closing dynamics of ion channels. It has long been known that the gate-based Langevin approach is not sufficiently accurate to reproduce the statistics of stochastic channel dynamics in Hodgkin–Huxley neurons. Here, we introduce a modified gate-based Langevin approach with rescaled noise strength to simulate stochastic channel dynamics. The rescaled independent gate and identical gate Langevin approaches improve the statistical results for the mean membrane voltage, inter-spike interval, and spike amplitude.
基金supported by the National Natural Science Foundation of China (Grant No.91338201)
文摘Satellite communication systems(SCS) operating on frequency bands above 10 GHz are sensitive to atmosphere physical phenomena, especially rain attenuation. To evaluate impairments in satellite performance, stochastic dynamic modeling(SDM) is considered as an effective way to predict real-time satellite channel fading caused by rain. This article carries out a survey of SDM using stochastic differential equations(SDEs) currently in the literature. Special attention is given to the different input characteristics of each model to satisfy specific local conditions. Future research directions in SDM are also suggested in this paper.
基金supported by the NSFC(10971225, 11171125, 91130003 and 11028102)the NSFH (2011CDB289)+1 种基金HPDEP (20114503 and 2011B400)the Cheung Kong Scholars Program and the Fundamental Research Funds for the Central Universities, HUST(2010ZD037)
文摘Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10572021 and 10372053）, and Fundamental Research Foundation of Beijing Institute of Technology, China （Grant No BIT-UBF-200507A4206）
文摘In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail. Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether＇s theorem.
文摘Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions on the bilayer square lattice under a time varying （sinusoidal） magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic （FM/FM） and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.
基金Project supported by the National Natural Science Foundation of China(Grant No.11172234)the Scholarship from China Scholarship Council(Grant No.201506290092)
文摘In order to improve the transform efficiency of bi-stable energy harvester（BEH）,this paper proposes an advanced bi-stable energy harvester（ABEH）,which is composed of two bi-stable beams coupling through their magnets.Theoretical analyzes and simulations for the ABEH are carried out.First,the mathematical model is established and its dynamical equations are derived.The formulas of magnetic force in two directions are given.The potential energy barrier of ABEH is reduced and the snap-through is liable to occur between potential wells.To demonstrate the ABEH＇s advantage in harvesting energy,comparisons between the ABEH and the BEH are carried out for both harmonic and stochastic excitations.Our results reveal that the ABEH＇s inter-well response can be elicited by a low-frequency excitation and the harvester can attain frequent jumping between potential wells at fairly weak random excitations.Thus,it can generate a higher output power.The present findings prove that the ABEH is preferable in harvesting energy and can be optimally designed such that it attains the best harvesting performance.
基金Project supported by the Research Foundation from Ministry of Education of China (Grant No 306020)the Specialized Research Fund for the Doctoral Program of Higher Education,China (Grant No 20060003050)the National Natural Science Foundation of China (Grant No 20773073)
文摘The highly excited vibrational levels of HCO in the electronic ground state, X^1A＇, are employed to determine the coefficients of an algebraic Hamiltonian, by which the dynamical potential is derived and shown to be very useful for interpreting the intramolecular vibrational relaxation （IVR） which operates via the HCO bending motion. The IVR inhibits the dissociation of H atom and enhances the stochastic degree of dynamical character. This approach is from a global viewpoint on a series of levels classified by the polyad number which is a constant of motion in a certain dynamical domain. In this way, the seemingly complicated level structure shows very regular picture, dynamically.
基金supported in part by the 985 Project of Shanghai Jiao Tong University,China
文摘Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named ＂the equation of life＂. Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerfu! Boltzmann-Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology.
文摘The dynamic magnetic behavior of the kinetic metamagnetic spin-5/2 Blume-Capel model is examined, within a mean-field approach, under a time-dependent oscillating magnetic field. To describe the kinetics of the system, Glauber- type stochastic dynamics has been utilized. The mean-field dynamic equations of the model are obtained from the Master equation. Firstly, these dynamic equations are solved to find the phases in the system. Then, the dynamic phase transition temperatures are obtained by investigating the thermal behavior of dynamic sublattice magnetizations. Moreover, from this investigation, the nature of the phase transitions （first- or second-order） is characterized. Finally, the dynamic phase diagrams are plotted in five different planes. It is found that the dynamic phase diagrams contain the paramagnetic （P）, antiferromagnetic （AF5/2, AF3/2, AF1/2） phases and five different mixed phases. The phase diagrams also display many dynamic critical points, such as tricritical point, triple point, quadruple point, double critical end point and separating point.
