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

LIU Chao; LI Yuan-Ke

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

LIU Chao 1, LI Yuan-Ke 2

1. Institute of Systems Science, Northeastern University, Shenyang 110004

2. School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao, 066004

*Correspondence author

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Funding: （No.20110042120016）, （No.XNK201301）, （No.F2011501023）

Opened online:12 May 2014

Accepted by: none

Citation: LIU Chao, LI Yuan-Ke.Global Stability Analysis of a Nonautonomous Stage Structured Competitive System with Toxic Effect and Double Maturation Delays[OL]. [12 May 2014] http://en.paper.edu.cn/en_releasepaper/content/4594672

In this paper, a nonautonomous stage structured two-species competitive system with toxic effect and double time delays is investigated due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and theinhibiting 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.

Keywords:Operations research and control theory; global stability analysis；periodic solution；maturation delay；toxic effect

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