Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching

• Drive–response concept and general feedback controller are used.
• White noise and color noise are considered in the response network.
• A new approach combining Lyapunov method and some graph theory is presented.
• Moment and almost sure exponential synchronization criteria are obtained.
• Stochastic Cohen–Grossberg neural networks with Markovian switching are studied.

In this paper, the issue of exponential synchronization for a class of stochastic coupled networks with Markovian switching is investigated. Based on some results in graph theory, Lyapunov stability theory and state feedback control technique, several sufficient criteria have been derived to ensure the pth moment exponential stability and almost sure exponential stability for the error network. That is, under these sufficient criteria, drive–response coupled networks can be pth moment exponentially synchronized and almost surely exponentially synchronized, respectively. Finally, stochastic Cohen–Grossberg neural networks with Markovian switching is employed to illustrate our feasible results.