Existence and stability of periodic solution for BAM neural networks with discontinuous neuron activations

In this paper, by using the fixed point theorem of differential inclusion theory and constructing suitable Lyapunov functions, the existence, uniqueness and global exponential stability of the periodic solution for BAM neural networks with discontinuous neuron activations are investigated. Moreover, the global convergence in finite time of the networks is discussed. The conditions that ensure the existence and stability of periodic solution are given. The obtained results extend previous work on global stability of BAM neural networks with Lipschitz continuous neuron activations but without delays, and show that Forti’s conjecture is true for BAM neural networks without delays.