Global exponential stability of neural networks with non-smooth and impact activations

Authors:
M. U. Akhmet;E. YıLmaz
Affiliations:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey;Department of Mathematics, Adnan Menderes University, 09010 Aydın, Turkey and Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Venue:
Neural Networks
Year:
2012

Citing 12
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Abstract

In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential stability of the solution is investigated. Examples with numerical simulations are given to validate the theoretical results.