A graph-theoretic approach to boundedness of stochastic Cohen–Grossberg neural networks with Markovian switching

• White noise and color noise are considered in the novel stochastic neural networks.
• A new approach combining Lyapunov method and some graph theory is presented.
• The sufficient principle obtained by using M-matrix technique is easy to be verified.
• The impact of Markovian switching and coupled structure are showed by two examples.

In this paper, a novel class of stochastic Cohen–Grossberg neural networks with Markovian switching (SCGNNMSs) is investigated, where the white noise and the color noise are taken into account. By utilizing Lyapunov method, some graph theory and M-matrix technique, several sufficient conditions are obtained to ensure the asymptotic boundedness of the SCGNNMSs. These criteria have a close relation to the topology property of the network and are easy to be verified in practice. Two numerical examples are also presented to substantiate the theoretical results.