Synchronized stationary distribution of hybrid stochastic coupled systems with applications to coupled oscillators and a Chua's circuits network

In this paper, the existence of synchronized stationary distribution for hybrid stochastic coupled systems (HSCSs) (here, also known as stochastic coupled systems with Markovian switching) is concerned. By the existence theory of stationary distribution as well as Lyapunov method and graph theory, two kinds of sufficient criteria are presented to promise the existence of synchronized stationary distribution for HSCSs. Our results exhibit that the existence region of synchronized stationary distribution has a close relationship with the intensity of stochastic perturbation. And when stochastic perturbation vanishes, synchronized stationary distribution will become complete synchronization. Then the proposed theoretical results are successfully applied to stochastic coupled oscillators and a Chua's circuits network. Some existence criteria of synchronized stationary distribution are also obtained. The corresponding numerical simulations are carried out to verify the validity of the theoretical results.