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Global Stability Analysis of a Nonautonomous Stage‐Structured Competitive System with Toxic Effect and Double Maturation Delays

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  • Chao Liu
  • Yuanke Li

Abstract

We investigate a nonautonomous two‐species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.

Suggested Citation

  • Chao Liu & Yuanke Li, 2014. "Global Stability Analysis of a Nonautonomous Stage‐Structured Competitive System with Toxic Effect and Double Maturation Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:689573
    DOI: 10.1155/2014/689573
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    References listed on IDEAS

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    1. Zhang, Hui & Li, Yingqi & Jing, Bin & Zhao, Weizhou, 2014. "Global stability of almost periodic solution of multispecies mutualism system with time delays and impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1138-1150.
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    Cited by:

    1. Liqiong Pu & Xiangdong Xie & Fengde Chen & Zhanshuai Miao, 2016. "Extinction in Two‐Species Nonlinear Discrete Competitive System," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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