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The Method of Lyapunov Functions: RNNs

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Neural Networks with Discontinuous/Impact Activations

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 9))

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Abstract

In this chapter, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of RNNs. The model involves alternating argument. Sufficient conditions are obtained for global exponential stability of the equilibrium point. Examples with numerical simulations are presented to illustrate the results.

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University (METU) Üniversiteler Mah. Dumlupinar, Ankara, Turkey

    Marat Akhmet

  2. Department of Mathematics, Adnan Menderes University Merkez Kampüsü Aytepe Mevkii, Aydın, Turkey

    Enes Yılmaz

Authors
  1. Marat Akhmet
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  2. Enes Yılmaz
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Akhmet, M., Yılmaz, E. (2014). The Method of Lyapunov Functions: RNNs. In: Neural Networks with Discontinuous/Impact Activations. Nonlinear Systems and Complexity, vol 9. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8566-7_7

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  • DOI: https://doi.org/10.1007/978-1-4614-8566-7_7

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8565-0

  • Online ISBN: 978-1-4614-8566-7

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