Title: Multiple almost periodic solutions in nonautonomous delayed neural networks
Authors: Lin, Kuang-Hui
Shih, Chih-Wen
應用數學系
Department of Applied Mathematics
Issue Date: 1-Dec-2007
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 2(n) exponentially stable sets. In addition, we establish the existence of 2(n) 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.
URI: http://dx.doi.org/10.1162/neco.2007.19.12.3392
http://hdl.handle.net/11536/10071
ISSN: 0899-7667
DOI: 10.1162/neco.2007.19.12.3392
Journal: NEURAL COMPUTATION
Volume: 19
Issue: 12
Begin Page: 3392
End Page: 3420
Appears in Collections:Articles