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Hopf Bifurcation in a Delayed Equation with Diffusion Driven by Carrying Capacity

Author

Listed:
  • Yuanxian Hui

    (School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China)

  • Yunfeng Liu

    (Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China)

  • Zhong Zhao

    (School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China)

Abstract

In this paper, a delayed reaction–diffusion equation with carrying capacity-driven diffusion is investigated. The stability of the positive equilibrium solutions and the existence of the Hopf bifurcation of the equation are considered by studying the principal eigenvalue of an associated elliptic operator. The properties of the bifurcating periodic solutions are also obtained by using the normal form theory and the center manifold reduction. Furthermore, some representative numerical simulations are provided to illustrate the main theoretical results.

Suggested Citation

  • Yuanxian Hui & Yunfeng Liu & Zhong Zhao, 2022. "Hopf Bifurcation in a Delayed Equation with Diffusion Driven by Carrying Capacity," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2382-:d:857244
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    References listed on IDEAS

    as
    1. Ma, Zhan-Ping & Huo, Hai-Feng & Xiang, Hong, 2017. "Hopf bifurcation for a delayed predator–prey diffusion system with Dirichlet boundary condition," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 1-18.
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