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Hopf bifurcation analysis of a diffusive single species model with stage structure and strong Allee effect

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  • Hao, Pengmiao
  • Wang, Xuechen
  • Wei, Junjie

Abstract

A diffusive single species model with stage structure and strong Allee effect subject to homogeneous Neumann boundary condition is considered. The stability of the nonnegative equilibria and the existence of Hopf bifurcation are investigated by analyzing the corresponding characteristic equation. Moreover, by the theory of normal form and center manifold, the stability and direction of bifurcating periodic solutions are determined. Finally, some numerical simulations are carried out.

Suggested Citation

  • Hao, Pengmiao & Wang, Xuechen & Wei, Junjie, 2018. "Hopf bifurcation analysis of a diffusive single species model with stage structure and strong Allee effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 153(C), pages 1-14.
    • Handle: RePEc:eee:matcom:v:153:y:2018:i:c:p:1-14
    DOI: 10.1016/j.matcom.2018.05.004
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    1. Malthus, Thomas Robert, 1798. "An Essay on the Principle of Population," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number malthus1798.
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    1. Djilali, Salih, 2019. "Impact of prey herd shape on the predator-prey interaction," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 139-148.
    2. Peng, Miao & Zhang, Zhengdi & Qu, Zifang & Bi, Qinsheng, 2020. "Qualitative analysis in a delayed Van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    3. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.

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