Stochastic Hopf bifurcation analysis in a stochastic lagged logistic discrete-time system with Poisson distribution coefficient

Ma, Shuping; Dong, Duan; Yang, Maosong

doi:10.1007/s11071-014-1866-3

Cited by 3 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Li and Fang et al [18][19][20][21] have developed the orthogonal polynomial method to approximate the dynamics response of linear random structure by a series of orthogonal basis functions. Owing to the representation of random parameters as random fields greatly increases the size and complexity of the analysis, Ma et al [22][23][24][25] have applied the method of orthogonal polynomial approximation to study various dynamics behaviors of nonlinear systems with random parameter idealized as random variables and have verified this method as feasible and effective.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation of Compound Stochastic van der Pol System

Ma¹,

Zhang²

2016

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L) expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strengthδand noise intensityσon stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increasedδcan relocate the critical value of bifurcation parameter forward while increasedσmakes it backward and the influence ofδis more sensitive thanσ. The results are verified by numerical simulations.

show abstract

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation of Compound Stochastic van der Pol System

Ma¹,

Zhang²

2016

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

Hopf bifurcation of nonlinear system with multisource stochastic factors

Bai

Zhang

et al. 2023

Theoretical and Applied Mechanics Letters

View full text Add to dashboard Cite

Control Analysis of Stochastic Lagging Discrete Ecosystems

Zhang

2022

Symmetry

View full text Add to dashboard Cite

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial approximation theory, the stochastic lagged discrete ecosystems are approximately transformed as its equivalent deterministic ecosystem. Based on the stability and bifurcation theory of deterministic discrete systems, through mathematical analysis, asymptotic stability and Hopf bifurcation are existent in the ecosystem, constructing control functions, controlling the behavior of the system dynamics. Finally, the effects of different random strengths on the bifurcation control and asymptotic stability control are verified by numerical simulations, which validate the correctness and effectiveness of the main results of this paper.

show abstract

Stochastic Hopf bifurcation analysis in a stochastic lagged logistic discrete-time system with Poisson distribution coefficient

Cited by 3 publications

References 26 publications

Hopf Bifurcation of Compound Stochastic van der Pol System

Hopf Bifurcation of Compound Stochastic van der Pol System

Hopf bifurcation of nonlinear system with multisource stochastic factors

Control Analysis of Stochastic Lagging Discrete Ecosystems

Contact Info

Product

Resources

About