×

Global stability analysis for stochastic coupled reaction-diffusion systems on networks. (English) Zbl 1263.93195

Summary: Coupled Systems on Networks (CSNs) can be used to model many real systems, such as food webs, ecosystems, metabolic pathways, the Internet, World Wide Web, social networks, and global economic markets. This paper is devoted to investigation of the stability problem for some Stochastic Coupled Reaction–Diffusion Systems on Networks (SCRDSNs). A systematic method for constructing global Lyapunov function for these SCRDSNs is provided by using graph theory. The stochastic stability, asymptotically stochastic stability and globally asymptotically stochastic stability of the systems are investigated. The derived results are less conservative than the results recently presented in Q. Luo, Y. Zhang [”Almost sure exponential stability of stochastic reaction diffusion systems”, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, e-Suppl., e487-e493 (2009; Zbl 1238.60065)]. In fact, the system discussed in [loc. cit.] is a special case of ours. Moreover, our novel stability principles have a close relation to the topological property of the networks. Our new method which constructs a relation between the stability criteria of a CSN and some topology property of the network, can help analyzing the stability of the complex networks by using the Lyapunov functional method.

MSC:

93D20 Asymptotic stability in control theory
93E03 Stochastic systems in control theory (general)
35K57 Reaction-diffusion equations
35R60 PDEs with randomness, stochastic partial differential equations

Citations:

Zbl 1238.60065
PDFBibTeX XMLCite
Full Text: DOI