Abstract
In this paper we discuss a randomized predator-prey dynamical system, which is composed of several patches connected by linear diffusion. Firstly, the situation that the positive solution of this system will not explode to infinity in a finite time according to lyapunov method is presented. Secondly, the results calculated by lyapunov functions and graph theory are demonstrated that the positive equilibrium is a global-stability under simple assumptions. Finally, the performance of this method is analyzed, and the existing results are proved to be improved.
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