Tbilisi Mathematical Journal

Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals

Swati Tyagi, Syed Abbas, Manuel Pinto, and Daniel Sepúlveda

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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.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 1 (2017), 171-196.

Dates
Received: 9 July 2016
Accepted: 12 August 2016
First available in Project Euclid: 26 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1527300025

Digital Object Identifier
doi:10.1515/tmj-2017-0012

Mathematical Reviews number (MathSciNet)
MR3627156

Zentralblatt MATH identifier
1362.26007

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 92B20: Neural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx] 34K07: Theoretical approximation of solutions 34A45: Theoretical approximation of solutions {For numerical analysis, see 65Lxx}

Keywords
Fractional-order Neural network Mittag-Leffer stability Approximate solution Error analysis Piecewise constant argument of generalized type

Citation

Tyagi, Swati; Abbas, Syed; Pinto, Manuel; Sepúlveda, Daniel. Uniform Euler approximation of solutions of fractional-order delayed cellular neural network on bounded intervals. Tbilisi Math. J. 10 (2017), no. 1, 171--196. doi:10.1515/tmj-2017-0012. https://projecteuclid.org/euclid.tbilisi/1527300025


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