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Convergence results in a well-known delayed predator-prey system. (English) Zbl 0876.92021
Summary: We provide a detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka-Volterra type predator-prey system with a single discrete delay. Our procedure requires the delay length to be small. A detailed example is presented. The method used here is to construct a proper Lyapunov functional in a restricted region.

MSC:
92D40 Ecology
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
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