研究了 Van der Pol-Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数 ,用多尺度法分离系统的快变项 ,讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明 ,当随机激...研究了 Van der Pol-Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数 ,用多尺度法分离系统的快变项 ,讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明 ,当随机激励强度增大时 ,系统的响应可从一个极限环变为一个扩散的极限环 ;在一定的条件下 ,系统可有两个稳定的稳态解及随机跳跃现象。展开更多
Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From th...Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included.展开更多
This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment sta...This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.展开更多
文摘研究了 Van der Pol-Duffing振子在简谐与随机噪声联合激励下的响应问题。用参数变换法使方程出现小参数 ,用多尺度法分离系统的快变项 ,讨论系统的阻尼项、非线性项和随机项等参数对系统响应的影响。理论分析和数值模拟表明 ,当随机激励强度增大时 ,系统的响应可从一个极限环变为一个扩散的极限环 ;在一定的条件下 ,系统可有两个稳定的稳态解及随机跳跃现象。
基金supported by the National Natural Science Foundation of China (Grant Nos.10932009 and 11172233)the Natural Science Foundation of Shaanxi Province (Grant No.2012JQ1004)the Northwestern Polytechnical University Foundation for Fundamental Research (Grant Nos.JC201266 and JC20110228)
文摘Stochastic bifurcations of the SD （smooth and discontinuous） oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072107 and 91016022)the Specialized Research Fund for the Doctoral Program of Higher Education of China (GrantNo.20093218110003)
文摘This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.
