Abstract
A two-species Lotka- Volterra system with time delays and diffusions is considered in the paper, in which both the prey and predator can independently diffuse among $n$ patches. By combining graph theory, a global Lyapunov functional for the two-species Lotka- Volterra system is provided. The globally asymptotical Stability of the equilibrium under some suitable conditions is shown. Finally, the theoretical results are illustrated by a numerical example.
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