Well-posedness of stochastic multi-weighted complex networks with regime-switching diffusions

Abstract

In this paper, a stochastic multi-weighted complex network with regime-switching diffusions (SMCNRSD) is considered. Here, the jump and the diffusion processes are interdependent, which generalizes the most existing network model. In the study of stochastic multi-weighted complex networks, stability analysis is an important topic. But so far, some work on stability requires stochastic multi-weighted complex networks to satisfy the global linear growth condition, which can not be applied to some high-order or nonlinear networks. Therefore, one of the research contents of this study is to obtain the global existence and uniqueness of SMCNRSD under local conditions. Besides, the SMCNRSD usually does not stabilize spontaneously for reasons such as stochastic disturbance, multiple weights and nonlinear coupling. To stabilize SMCNRSD, periodic intermittent control is introduced to obtain the stability criterion. In application, stochastic multi-weighted Chua’s circuits with regime-switching diffusions are taken into account. The corresponding existence and uniqueness as well as stability criteria are given under local conditions. To further illustrate the validity of theoretical results, numerical simulations are given.