On input-to-state stability for stochastic multi-group models with multi-dispersal

Abstract

This paper focuses on the input-to-state stability for a general class of stochastic multi-group models with multi-dispersal. By incorporating graph theory with Lyapunov method as well as stochastic analysis techniques, novel sufficient criteria are derived, which are in the form of Lyapunov-type theorem and coefficient-type criterion, respectively. Moreover, to show the applicability of our findings, we employ coefficient-type criterion to analyze the input-to-state stability for stochastic coupled oscillators. Finally, a numerical example and its simulations are offered to demonstrate the validity and feasibility of the theoretic results.

Keywords:

• Input-to-state stability
• stochastic multi-group models
• multi-dispersal
• graph theory

AMS Subject Classifications:

• 45R05
• 60H20
• 93D05

Acknowledgements

The authors really appreciate the referees’ valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by grants from the National Natural Science Foundation of China [grant number 11271101], [grant number 11501150].