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Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

Author

Listed:
  • Xiao, Min
  • Jiang, Guoping
  • Zhao, Lindu
  • Xu, Wenying
  • Wan, Youhong
  • Fan, Chunxia
  • Wang, Zhengxin

Abstract

The dynamical behaviors of an isolated population model involving delay-dependent parameters are investigated. It is shown that the positive equilibrium switches from being stable to unstable and then back to stable as the delay increases, and the Hopf bifurcation occurs finite times between the two critical values of stability changes which can be analytically determined. Moreover, the bifurcating periodic solutions are expressed analytically in an approximate form by the perturbation approach and Floquet technique. The direction and stability of the bifurcating periodic solutions are also determined. Finally, the validity of the results is shown by the consistency with the numerical simulations.

Suggested Citation

  • Xiao, Min & Jiang, Guoping & Zhao, Lindu & Xu, Wenying & Wan, Youhong & Fan, Chunxia & Wang, Zhengxin, 2015. "Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 99-115.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:99-115
    DOI: 10.1016/j.amc.2015.04.071
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    Cited by:

    1. Zhu, Linhe & Liu, Mengxue & Li, Yimin, 2019. "The dynamics analysis of a rumor propagation model in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 118-137.
    2. Zarei, Amin & Tavakoli, Saeed, 2016. "Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 323-339.

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