Multiple periodic solutions of delayed competitive neural networks via functional differential inclusions

In this paper, a class of general competitive neural networks with discontinuous right-hand sides and mixed time delays is investigated. Based on functional differential inclusions theory and fixed point theorem of set-valued maps, the existence of one and multiple positive periodic solutions for the competitive neural networks are obtained. Without assuming the boundedness or satisfying a growth condition of discontinuous neuron activation functions, the results on the existence of one and multiple positive periodic solutions will also be valid. Some numerical examples are given to show the applicability and effectiveness of our main results.