Expinential Stability Of Coupled Stochastic Retarded Systems On Networks

Over the past decades, different classes of coupled systems on networks haveattracted the attention of researchers, due to their wide applications in chemistry,ecology model, and the infectious disease model. Researchers have reached manyclassic conclusions by analyzing the stability of complex coupled systems with differentmethods, which has promoted the development of the investigation. In this thesis, theexponential stability for stochastic functional differential equations on networks and theexponential stability for stochastic neutral differential equations on networks areinvestigated.Firstly, based on the graph theory and Razumikhin technique, the exponentialstability and the almost surely exponential stability for stochastic functional differentialequations on networks is investigate, and the sufficient conditions ensure the stability ofthe system is obtained. Furthermore, as an illustrative example of applications of ourabove results, we consider a stochastic varying delay coupled systems on networks. Atthe same time, a numerical example is used to verify the effectiveness of the developedtheory.Secondly, the exponential stability for stochastic neutral differential equations onnetworks is investigated. In this part, we change the form of neutral differentialequations on networks by applying the properties of special inequality. We also useRazumikhin technique combined with graph theory method and the properties of specialinequality to extend our above results to the coupled stochastic neutral systems. Thesufficient conditions for the exponential stability of the systems are obtained tocomplete the proof of theorem by demonstration. Finally, we use the conclusions of thetheorem to application.