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Convergence of solutions for Volterra-Lotka prey-predator systems with time delays. (English) Zbl 1163.34303
Summary: This work is concerned with \(N\)-species prey-predator systems with time delays. The aim of this work is to obtain a sufficient condition for asymptotic behavior of the time-dependent solution and the existence of a positive steady-state solution. The result of global asymptotic stability implies that all of the model systems coexist; the trivial and all kinds of semitrivial solutions are unstable.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
92D25 Population dynamics (general)
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