Title :
Graph Theory-Based Approach for Stability Analysis of Stochastic Coupled Systems With Lévy Noise on Networks
Author :
Chunmei Zhang ; Wenxue Li ; Ke Wang
Author_Institution :
Dept. of Math., Harbin Inst. of Technol., Harbin, China
Abstract :
In this paper, a novel class of stochastic coupled systems with Lévy noise on networks (SCSLNNs) is presented. Both white noise and Lévy noise are considered in the networks. By exploiting graph theory and Lyapunov stability theory, criteria ensuring pth moment exponential stability and stability in probability of these SCSLNNs are established, respectively. These principles are closely related to the topology of the network and the perturbation intensity of white noise and Lévy noise. Moreover, to verify the theoretical results, stochastic coupled oscillators with Lévy noise on a network and stochastic Volterra predator-prey system with Lévy noise are performed. Finally, a numerical example about oscillators´ network is provided to illustrate the feasibility of our analytical results.
Keywords :
Lyapunov methods; asymptotic stability; graph theory; perturbation techniques; predator-prey systems; probability; stability criteria; stochastic systems; white noise; Lyapunov stability theory; SCSLNN; graph theory-based approach; network topology; perturbation intensity; probability; pth moment exponential stability criteria; stochastic Volterra predator-prey system; stochastic coupled oscillators; stochastic coupled system-with-Lévy noise on networks; white noise; Graph theory; Lyapunov methods; Numerical stability; Stability analysis; Stochastic processes; White noise; Lévy noise; L??vy noise; networks; stability; stochastic coupled systems;
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
DOI :
10.1109/TNNLS.2014.2352217