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Stability analysis of recurrent neural networks with piecewise constant argument of generalized type
Date
2010-09-01
Author
Akhmet, Marat
Yılmaz, Elanur
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In this paper, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of recurrent neural networks (RNNs). The model involves both advanced and delayed arguments. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results.
Subject Keywords
Neural networks
,
Piecewise constant argument of generalized type
URI
https://hdl.handle.net/11511/31600
Journal
NEURAL NETWORKS
DOI
https://doi.org/10.1016/j.neunet.2010.05.006
Collections
Graduate School of Social Sciences, Article
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We address differential equations with piecewise constant argument of generalized type [5-8] and investigate their stability with the second Lyapunov method. Despite the fact that these equations include delay, stability conditions are merely given in terms of Lyapunov functions; that is, no functionals are used. Several examples, one of which considers the logistic equation, are discussed to illustrate the development of the theory. Some of the results were announced at the 14th International Congress on C...
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In this paper we introduce an impulsive Hopfield-type neural network system with piecewise constant argument of generalized type. Sufficient conditions for the existence of the unique equilibrium are obtained. Existence and uniqueness of solutions of such systems are established. Stability criterion based on linear approximation is proposed. Some sufficient conditions for the existence and stability of periodic solutions are derived. An example with numerical simulations is given to illustrate our results.
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M. Akhmet and E. Yılmaz, “Stability analysis of recurrent neural networks with piecewise constant argument of generalized type,”
NEURAL NETWORKS
, pp. 805–811, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31600.