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Dynamics of two-species delayed competitive stage-structured model described by differential-difference equations. (English) Zbl 1430.34093

Summary: Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
92D40 Ecology
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
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