Existence and global stability of a periodic solution for a cellular neural network

• Sufficient conditions for existence of periodic solution for CNN is derived.
• Sufficient conditions for global stably and uniqueness of periodic solution are given.
• Numerical simulation is given to verify the effectiveness of proposed approach.
• Every detailed information refer to simulation is given.

Purpose of this study is to investigate the dynamical properties of Chua and Yang cellular neural networks (CNNs). Based on the continuation theorem of coincidence degree theory, a novel sufficient condition with respect to the existence of periodic solution for CNNs is derived. Moreover, a generalized Lyapunov–Krasovskii functional is designed to guarantee the global stability of the existed periodic solution. An illustrative example is given to verify the effectiveness and correctness of the proposed method, furthermore, random disturbance is added in the numerical simulation in order to verify the robustness of the proposed approach.