Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay.

In this paper, the input-to-state stability (ISS) for a general class of stochastic multi-group models with multi-dispersal and time-varying delay is investigated. By means of graph theory and Lyapunov method as well as stochastic analysis techniques, sufficient criteria including a Lyapunov-type theorem and a coefficient-type theorem are obtained to guarantee that the proposed model is input-to-state stable. In addition, to show the applicability of our findings, the coefficient-type theorem is employed to study the ISS of stochastic coupled oscillators with time-varying delay and control input. Finally, a numerical example is offered to illustrate the effectiveness of the theoretical results.