Global asymptotic dynamics of a class of  nonlinearly coupled neural networks  with delays

Jui-Pin Tseng

doi:10.3934/dcds.2013.33.4693

Article Contents

2013, Volume 33, Issue 10: 4693-4729. Doi: 10.3934/dcds.2013.33.4693

This issue Previous Article Continuity of Hausdorff measure for conformal dynamical systems Next Article Expansion growth, entropy and invariant measures of distal groups and pseudogroups of homeo- and diffeomorphisms

Global asymptotic dynamics of a class of nonlinearly coupled neural networks with delays

Jui-Pin Tseng^1,

1.
Department of Applied Mathematics, National Pingtung University of Education, Pingtung 900

Received: August 31, 2012

Revised: December 31, 2012

Published: September 2013

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Abstract

This work presents an effective approach to the study of the global asymptotic dynamics of general coupled systems. Under the developed framework, the problem of establishing global synchronization or global convergence reduces to solving a corresponding system of linear equations. We illustrate this approach with a class of neural networks that consist of a pair of sub-networks under various types of nonlinear and delayed couplings. We study both the synchronization and the asymptotic synchronous phases of the dynamics, including global convergence to zero, global convergence to multiple synchronous equilibria, and global synchronization with nontrivial synchronous periodic solutions. Our investigation also provides theoretical support to some numerical findings, and improves or extend some results in the literature.

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Mathematics Subject Classification: Primary: 34K20, 92B20; Secondary: 34K18, 92C20.

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