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Steady state bifurcation of a population model with chemotaxis

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  • Chen, Mengxin
  • Zheng, Qianqian

Abstract

In this paper, we are concerned with the pattern dynamics of a population model with chemotaxis. The existence of the solution and the global stability of the coexistence equilibrium are performed. In the sequel, we find that chemotaxis can induce the steady state bifurcation of the spatiotemporal model, and there are multiple thresholds of the steady state bifurcation with different assumptions. We then give the amplitude equation to determine the direction of the steady state bifurcation via the multiple time scales. It is found that the population model admits the supercritical or subcritical steady state bifurcation. Numerical results check the validity of the theoretical analysis.

Suggested Citation

  • Chen, Mengxin & Zheng, Qianqian, 2023. "Steady state bifurcation of a population model with chemotaxis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    • Handle: RePEc:eee:phsmap:v:609:y:2023:i:c:s0378437122009396
    DOI: 10.1016/j.physa.2022.128381
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    References listed on IDEAS

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    1. Chen, Mengxin & Zheng, Qianqian, 2022. "Predator-taxis creates spatial pattern of a predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Tian, Canrong & Ling, Zhi & Zhang, Lai, 2020. "Delay-driven spatial patterns in a network-organized semiarid vegetation model," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Debgopal Sahoo & Guruprasad Samanta & Manuel De la Sen & Xiaohua Ding, 2021. "Impact of Fear and Habitat Complexity in a Predator-Prey System with Two Different Shaped Functional Responses: A Comparative Study," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-22, September.
    4. Duan, Daifeng & Niu, Ben & Wei, Junjie, 2019. "Hopf-Hopf bifurcation and chaotic attractors in a delayed diffusive predator-prey model with fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 206-216.
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    Cited by:

    1. Chen, Mengxin & Srivastava, Hari Mohan, 2023. "Stability of bifurcating solution of a predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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