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Multiple Almost Periodic Solutions in Nonautonomous Delayed Neural Networks

hs3893{at}mail.nc.hcc.edu.tw Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.

Chih-Wen Shih

cwshih{at}math.nctu.edu.tw Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2ⁿ exponentially stable sets. In addition, we establish the existence of 2ⁿ exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.