Symmetry-breaking bifurcation analysis of stochastic van der pol system via Chebyshev polynomial approximation

Shaojuan Ma; Wei Xu; Yanfei Jin; Wei Li; Tong Fang

doi:10.1016/j.cnsns.2005.03.004

Symmetry-breaking bifurcation analysis of stochastic van der pol system via Chebyshev polynomial approximation

Shaojuan Ma^*, Wei Xu, Yanfei Jin, Wei Li, Tong Fang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

Chebyshev polynomial approximation is applied to the symmetry-breaking bifurcation problem of a stochastic van der Pol system with bounded random parameter subjected to harmonic excitation. The stochastic system is reduced into an equivalent deterministic system, of which the responses can be obtained by numerical methods. Nonlinear dynamical behaviors related to various forms of stochastic bifurcations in stochastic system are explored and studied numerically.

Original language	English
Pages (from-to)	366-378
Number of pages	13
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	12
Issue number	3
DOIs	https://doi.org/10.1016/j.cnsns.2005.03.004
Publication status	Published - Jun 2007
Externally published	Yes

Keywords

Chebyshev polynomial
Probability density function
Stochastic van der Pol system
Symmetry-breaking bifurcation

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10.1016/j.cnsns.2005.03.004

Cite this

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title = "Symmetry-breaking bifurcation analysis of stochastic van der pol system via Chebyshev polynomial approximation",

abstract = "Chebyshev polynomial approximation is applied to the symmetry-breaking bifurcation problem of a stochastic van der Pol system with bounded random parameter subjected to harmonic excitation. The stochastic system is reduced into an equivalent deterministic system, of which the responses can be obtained by numerical methods. Nonlinear dynamical behaviors related to various forms of stochastic bifurcations in stochastic system are explored and studied numerically.",

keywords = "Chebyshev polynomial, Probability density function, Stochastic van der Pol system, Symmetry-breaking bifurcation",

author = "Shaojuan Ma and Wei Xu and Yanfei Jin and Wei Li and Tong Fang",

year = "2007",

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doi = "10.1016/j.cnsns.2005.03.004",

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T1 - Symmetry-breaking bifurcation analysis of stochastic van der pol system via Chebyshev polynomial approximation

AU - Ma, Shaojuan

AU - Xu, Wei

AU - Jin, Yanfei

AU - Li, Wei

AU - Fang, Tong

PY - 2007/6

Y1 - 2007/6

N2 - Chebyshev polynomial approximation is applied to the symmetry-breaking bifurcation problem of a stochastic van der Pol system with bounded random parameter subjected to harmonic excitation. The stochastic system is reduced into an equivalent deterministic system, of which the responses can be obtained by numerical methods. Nonlinear dynamical behaviors related to various forms of stochastic bifurcations in stochastic system are explored and studied numerically.

AB - Chebyshev polynomial approximation is applied to the symmetry-breaking bifurcation problem of a stochastic van der Pol system with bounded random parameter subjected to harmonic excitation. The stochastic system is reduced into an equivalent deterministic system, of which the responses can be obtained by numerical methods. Nonlinear dynamical behaviors related to various forms of stochastic bifurcations in stochastic system are explored and studied numerically.

KW - Chebyshev polynomial

KW - Probability density function

KW - Stochastic van der Pol system

KW - Symmetry-breaking bifurcation

UR - http://www.scopus.com/inward/record.url?scp=33750512615&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2005.03.004

DO - 10.1016/j.cnsns.2005.03.004

M3 - Article

AN - SCOPUS:33750512615

SN - 1007-5704

VL - 12

SP - 366

EP - 378

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 3

ER -

Symmetry-breaking bifurcation analysis of stochastic van der pol system via Chebyshev polynomial approximation

Abstract

Keywords

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