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Jan 2017 Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals
Swati Tyagi, Syed Abbas, Manuel Pinto, Daniel Sepúlveda
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Tbilisi Math. J. 10(1): 171-196 (Jan 2017). DOI: 10.1515/tmj-2017-0012

Abstract

In this paper, we study convergence characteristics of a class of continuous time fractional-order cellular neural network containing delay. Using the method of Lyapunov and Mittag-Leffer functions, we derive sufficient condition for global Mittag-Leffer stability, which further implies global asymptotic stability of the system equilibrium. Based on the theory of fractional calculus and the generalized Gronwall inequality, we approximate the solution of the corresponding neural network model using discretization method by piecewise constant argument and obtain some easily verifiable conditions, which ensures that the discrete-time analogues preserve the convergence dynamics of the continuous-time networks. In the end, we give appropriate examples to validate the proposed results, illustrating advantages of the discrete-time analogue over continuous-time neural network for numerical simulation.

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Swati Tyagi. Syed Abbas. Manuel Pinto. Daniel Sepúlveda. "Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals." Tbilisi Math. J. 10 (1) 171 - 196, Jan 2017. https://doi.org/10.1515/tmj-2017-0012

Information

Received: 9 July 2016; Accepted: 12 August 2016; Published: Jan 2017
First available in Project Euclid: 26 May 2018

zbMATH: 1362.26007
MathSciNet: MR3627156
Digital Object Identifier: 10.1515/tmj-2017-0012

Subjects:
Primary: 26A33
Secondary: 34A45, 34K07, 92B20

Rights: Copyright © 2017 Tbilisi Centre for Mathematical Sciences

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Vol.10 • No. 1 • Jan 2017
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