Multistability and new attraction basins of almost-periodic solutions of delayed neural networks

Authors:
Lili Wang;Wenlian Lu;Tianping Chen
Affiliations:
Shanghai Key Laboratory for Contemporary Applied Mathematics and Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, ...;Shanghai Key Laboratory for Contemporary Applied Mathematics and Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, ...;Shanghai Key Laboratory for Contemporary Applied Mathematics and Key Laboratory of Nonlinear Science of Chinese Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, ...
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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Abstract

In this paper, we investigate multistability of almost-periodic solutions of recurrently connected neural networks with delays (simply called delayed neural networks). We will reveal that under some conditions, the space Rn can be divided into 2n subsets, and in each subset, the delayed -neuron neural network has a locally stable almost-periodic solution. Furthermore, we also investigate the attraction basins of these almost-periodic solutions. We reveal that the attraction basin of almost-periodic trajectory is larger than the subset, where the corresponding almost-periodic trajectory is located. In addition, several numerical simulations are presented to corroborate the theoretical results.