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Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delay. (English) Zbl 0661.92018

Lotka-Volterra models with continuous time delays are studied. The authors prove the boundedness of the solutions and the existence of a nonnegative equilibrium point for two different patches with multiple species connected by diffusion. In conclusion, the existence and global asymptotic stability of the equilibrium point for the model with identical patches and continuous time delays and for the symbiotic model with different patches and time delays are analyzed.
Reviewer: M.Gronychova

MSC:

92D25 Population dynamics (general)
34D99 Stability theory for ordinary differential equations
92D40 Ecology
34C11 Growth and boundedness of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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