Cluster synchronization stability for stochastic complex dynamical networks with probabilistic interval time-varying delays
Hongjie Li · Journal of Physics A Mathematical and Theoretical · 2011
The paper investigates the cluster synchronization stability problem for a class of complex dynamical networks with stochastic nonlinearities and probabilistic interval time-varying delays. The stochastic nonlinearities are considered here to reflect more realistic dynamical behaviors of complex networks; the delay in this paper is assumed to be random and its probability distribution is known a priori . Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent cluster synchronization stability criteria are derived in the form of linear matrix inequalities which can be readily solved by using the LMI toolbox in MATLAB; the solvability of derived conditions depends on not only the size of the delay but also the probability of the delay taking values in some intervals. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.