Stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks: A graph approach
Journal article, Peer reviewed
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Original versionKao, Y., & Karimi, H. R. (2014). Stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks: A graph approach. Abstract and Applied Analysis, 2014, 1-13. doi: 10.1155/2014/597502 10.1155/2014/597502
This paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. These stability principles have a close relation with the topology property of the network. We also provide a systematic method for constructing global Lyapunov function for these CSRDSNs by using graph theory. The new method can help to analyze the dynamics of complex networks. An example is presented to illustrate the effectiveness and efficiency of the obtained results.
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/597502 Open Access