Multiperiodicity of periodically oscillated discrete-time neural networks with transient excitatory self-connections and sigmoidal nonlinearities

Authors:
Zhenkun Huang;Xinghua Wang;Chunhua Feng
Affiliations:
School of Sciences, Jimei University, Xiamen, China;Department of Mathematics, Zhejiang University, Hangzhou, China;Department of Mathematics, Guangxi Normal University, Guilin, China
Venue:
IEEE Transactions on Neural Networks
Year:
2010

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Abstract

Abstract--The existing approaches to the multistability and multiperiodicity of neural networks rely on the strictly excitatory self-interactions of neurons or require constant interconnection weights. For periodically oscillated discrete-time neural networks (DTNNs), it is difficult to discuss multistable dynamics when the connection weights are periodically oscillated around zero. By using transient excitatory self-interactions of neurons and sigmoidal nonlinearities, we develop an approach to investigate multiperiodicity and attractivity of periodically oscillated DTNNs with time-varying and distributed delays. It shows that, under some new criteria, there exist multiplicity results of periodic solutions which are locally or globally exponentially stable. Computer numerical simulations are performed to illustrate the new theories.