Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

Abstract EN

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated.

By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure that n-dimensional Cohen-Grossberg neural networks with k-level discontinuous activation functions can have kn equilibrium points or kn periodic orbits.

Finally, several examples are given to illustrate the feasibility of the obtained results.