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Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel

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  • Zhang, Xiaofeng
  • Yuan, Rong

Abstract

Stochastic bifurcation theory plays an important role in stochastic dynamical systems, thus, in this paper, we mainly consider the stochastic bifurcation of a stochastic logistic model with distributed delay in the weak kernel case, where the birth rate of species is disturbed by white noise. In order to study the bifurcation of stochastic logistic system, we use the intrinsic growth rate of species as a bifurcation parameter. Firstly, we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model with distributed delay. Furthermore, by deriving the corresponding Fokker–Planck equation, we obtain the exact expression of the joint density function of the stochastic system near the positive equilibrium point. Finally, we give some conclusions.

Suggested Citation

  • Zhang, Xiaofeng & Yuan, Rong, 2022. "Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 56-70.
    • Handle: RePEc:eee:matcom:v:195:y:2022:i:c:p:56-70
    DOI: 10.1016/j.matcom.2021.12.023
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    References listed on IDEAS

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    1. Lv, Yehu & Liu, Zhihua, 2021. "Turing-Hopf bifurcation analysis and normal form of a diffusive Brusselator model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Sun, Xinguo & Zuo, Wenjie & Jiang, Daqing & Hayat, Tasawar, 2018. "Unique stationary distribution and ergodicity of a stochastic Logistic model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 864-881.
    3. Liu, Meng & Bai, Chuanzhi, 2015. "A remark on a stochastic logistic model with Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 521-526.
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