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Global stability in diffusive delay Lotka-Volterra systems. (English) Zbl 0752.34041

The authors investigate the diffusive delay Lotka-Volterra system occurring in models of population dynamics. They have constructed a Lyapunov function to obtain a sufficient condition for global asymptotic stability of the system studied by them. They give a discrete diffusive delay treatment of the Lotka-Volterra system. In the course of their investigations they study a system of ordinary differential equations with constant coefficients in connection with the system under study. Finally, they give a brief discussion of the work of a number of researchers having interaction with their work as well as various aspects of the well-known Lotka-Volterra system.

MSC:

34K30 Functional-differential equations in abstract spaces
35R10 Partial functional-differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
92D25 Population dynamics (general)
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