On the existence and stability of the periodic solution in the Cohen–Grossberg neural network with time delay and high-order terms

摘要

Qualitative property for a class of the delayed Cohen–Grossberg neural network with high-order terms is investigated in the paper. Periodic solution is rigorously proved to be exist in this class of models by means of the Gains and Mawhin’s continuation theorem. In addition, sufficient conditions are established for both global exponential and asymptotical stability of the existent periodic solution with the aid of the Lyapunov functional and the theory of linear matrix inequality (LMI). Finally, two examples with their numerical simulations are provided to illustrate the possible application of our criteria.