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Abstract and Applied Analysis
Volume 2014, Article ID 689573, 15 pages
Research Article

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

Chao Liu1,2 and Yuanke Li1,3

1Institute of Systems Science, Northeastern University, Shenyang 110004, China
2State Key Laboratory of Integrated Automation of Process Industry, Northeastern University, Shenyang 110004, China
3Institute of Information and Computational Science, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China

Received 25 February 2014; Revised 19 August 2014; Accepted 22 August 2014; Published 19 October 2014

Academic Editor: Zhiming Guo

Copyright © 2014 Chao Liu and Yuanke Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.