Stochastic stability for pantograph multi-group models with dispersal and stochastic perturbation

This paper focuses on a novel model of pantograph multi-group models with dispersal and stochastic perturbation. The effects of proportional delay, multiple dispersal among groups, and stochastic perturbation are all taken into account in this model. By means of combining graph theory with Lyapunov method, sufficient criteria are obtained to ensure the globally exponential stability of the model, which are in the forms of Lyapunov functions and the coefficients, respectively. Moreover, to show the applicability of our results, coefficient-type criterion is employed to stochastic coupled pantograph oscillators described by two digraphs successfully. Finally, a numerical example is offered to demonstrate the validity of the theoretic results.