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**Global stability analysis of a nonautonomous stage-structured competitive system with toxic effect and double maturation delays.**
*(English)*
Zbl 1474.92081

Summary: 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.

### MSC:

92D25 | Population dynamics (general) |

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\textit{C. Liu} and \textit{Y. Li}, Abstr. Appl. Anal. 2014, Article ID 689573, 15 p. (2014; Zbl 1474.92081)

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