Stochastic chaos in a Duffing oscillator and its control

Wu, Changying; Lei, Youming; Fang, Tong

doi:10.1016/j.chaos.2005.04.035

Cited by 30 publications

(18 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, effective numerical methods to solve such high dimensional Fokker-Planck equations in the large unbounded domain are still under development [2]. Instead, in this section, we generate the most probable phase portrait by sample-wise simulation (often called Monte-Carlo simulation) for the following Duffing oscillator with harmonic excitation and multiplicative noise [12,15] dx = ydt, dy = (γ 1 cos(wt) + a 1 x − a 2 y − a 3 x 3 )dt + γ 2 xdB t .…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Most probable dynamics of some nonlinear systems under noisy fluctuations

Cheng

Duan

Wang

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Section: Accepted Manuscriptmentioning

confidence: 99%

Most probable dynamics of some nonlinear systems under noisy fluctuations

Cheng

Duan

Wang

2016

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

“…The third method, introduced in [7,8], and improved by Li [9], is an effective analytical method [10,11]. Recently stochastic bifurcation and chaos in some typical dynamical models were successfully analyzed by the Chebyshev polynomial approximation [12,13], but there are few reports on stochastic synchronization so far.…”

Section: Introductionmentioning

confidence: 99%

Chaos Synchronization Between Two Stochastic Lorenz-family Systems

Lin

2010

2010 International Workshop on Chaos-Fractal Theories and Applications

View full text Add to dashboard Cite

In this paper, we address stochastic chaos synchronization of two stochastic Lorenz-family systems with bounded random parameters. In the analysis the stochastic Lorenz-family system is firstly transformed into an equivalent deterministic nonlinear system by the Chebyshev polynomial approximation, so that the chaos synchronization problem of stochastic Lorenz-family systems can be reduced into that of the equivalent deterministic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a series of simple feedback control laws are applied to two identical stochastic Lorenz-family systems. Numerical simulation shows the effectiveness of synchronous programs.

show abstract

“…The works [36][37][38] have illustrated that bifurcations and chaos in stochastic systems with random parameters are different from the deterministic system with their own features. Wu [39] has discussed in detail the chaos and its control via orthogonal polynomial approximation. So far, no study has explored the bifurcation control in this kind of a stochastic system.…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation control for stochastic dynamical system with nonlinear random feedback method

Zhang

2010

Nonlinear Dyn

View full text Add to dashboard Cite

Hopf bifurcation control in nonlinear stochastic dynamical system with nonlinear random feedback method is studied in this paper. Firstly, orthogonal polynomial approximation is applied to reduce the controlled stochastic nonlinear dynamical system with nonlinear random controller to the deterministic equivalent system, solvable by suitable numerical methods. Then, Hopf bifurcation control with nonlinear random feedback controller is discussed in detail. Numerical simulations show that the method provided in this paper is not only available to control the stochastic Hopf bifurcation in nonlinear stochastic dynamical system, but is also superior to the deterministic nonlinear feedback controller.

show abstract

Stochastic chaos in a Duffing oscillator and its control

Cited by 30 publications

References 11 publications

Most probable dynamics of some nonlinear systems under noisy fluctuations

Most probable dynamics of some nonlinear systems under noisy fluctuations

Chaos Synchronization Between Two Stochastic Lorenz-family Systems

Hopf bifurcation control for stochastic dynamical system with nonlinear random feedback method

Contact Info

Product

Resources

About