Group synchronization and control of a new class of adaptive complex network with Brownian Motion and Time-varying Delay

In this paper, the Group Mean Square Synchronization (GMSS) of a new class of adaptive Complex Dynamical Network (CDN) with Limited Stochastic Perturbation (LSP) and interval Time-Varying Delays (TVD) is investigated. The zero-mean real scalar Brownian Motion (BM) with LSP is also discussed. In this CDN, the weight configuration matrices are considered in two cases : TVD and Non-Time-Varying Delay (NTVD). The outer-coupling matrices are also assumed to be two cases : symmetric and dissymmetric. Based on the control theory and stochastic analysis such as : adaptive control method, Itô formula, Lyapunov Stability Theory (LST) and Kronecker product rules, the controllers nd adaptive schemes are constructed which let all nodes reach the GMSS asymptotically in the CDN. Finally, some examples of several complex chaotic systems are presented to demonstrate the proposed theoretical analysis.