Multiple almost periodic solutions in nonautonomous delayed neural networks

Authors:
Kuang-Hui Lin;Chih-Wen Shih
Affiliations:
Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. hs3893@mail.nc.hcc.edu.tw;Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. cwshih@math.nctu.edu.tw
Venue:
Neural Computation
Year:
2007

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Abstract

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.