6533b86efe1ef96bd12cc0a9

RESEARCH PRODUCT

Global stability of coupled Markovian switching reaction–diffusion systems on networks

Changhong WangRan BiHamid Reza KarimiYonggui Kao

subject

Lyapunov functionRelation (database)Computer Science Applications1707 Computer Vision and Pattern RecognitionTopology (electrical circuits)Graph theoryStochastic coupled systemsComplex networkStability (probability)Computer Science Applicationssymbols.namesakeControl and Systems EngineeringControl theoryReaction–diffusion systemNetworks; Reaction-diffusion; Stability; Stochastic coupled systems; Control and Systems Engineering; Analysis; Computer Science Applications1707 Computer Vision and Pattern RecognitionsymbolsApplied mathematicsNetworksReaction-diffusionMarkovian switchingStabilityAnalysisMathematics

description

Abstract In this paper, we investigate the stability problem for some Markovian switching reaction–diffusion coupled systems on networks (MSRDCSNs). By using the Lyapunov function, we establish some novel stability principles for stochastic stability, asymptotically stochastic stability, globally asymptotically stochastic stability and almost surely exponential stability of the MSRDCSNs. These stability principles have a close relation to the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these MSRDCSNs by using graph theory. The new method can help analyze the dynamics of complex networks.

yearjournalcountryeditionlanguage
2014-08-01Nonlinear Analysis: Hybrid Systems
https://doi.org/10.1016/j.nahs.2013.12.004