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Stability analysis for discrete-time coupled systems with multi-diffusion by graph-theoretic approach and its application

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  • In this paper, we investigate the global stability of discrete-time coupled systems with multi-diffusion (DCSMDs). By utilizing a multi-digraph theory, we construct a global Lyapunov function for DCSMDs. Consequently, some sufficient conditions are presented to ensure the stability of a general DCSMDs. Then the proposed theory is successfully applied to analyze the global stability for a discrete-time predator-prey model which is discretized by a nonstandard finite difference scheme. Finally, an example with numerical simulation is given to demonstrate the effectiveness of the obtained results.
    Mathematics Subject Classification: Primary: 39A30; Secondary: 37J25, 92B99.


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