Multiperiodicity and Attractivity Analysis for Discrete-Time Second Order Delayed Recurrent Neural Networks

This paper investigates the multiperiodicity and attractivity of discrete-time second order recurrent neural networks. Sufficient conditions are obtained for the existence of 2n locally attractive periodic orbits in an n-dimensional network. Also, the state space is divided into 3n regions and sufficient conditions are given to ensure that a periodic orbit belonging to one of these regions is locally or globally attractive. As particular cases, cellular neural networks and Hopfield neural networks are also investigated. Some numerical simulations are given which remarkably demonstrate the theoretical results.

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