On the stability and Lyapunov direct method for fractional difference model of BAM neural networks

Issue title: Mathematical Modelling in Computational and Life Sciences

Guest editors: Ahmed Farouk

Article type: Research Article

Authors: Alzabut, Jehad^a | Tyagi, Swati^{b; c; *} | Martha, S.C.^c

Affiliations: [a] Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia | [b] Department of Applied Sciences, Punjab Engineering College (PEC), Deemed to be University, Chandigarh, India | [c] Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab, India

Correspondence: [*] Corresponding author. Swati Tyagi. E-mail: styagi99@gmail.com.

Abstract:  We provide sufficient conditions for the existence, uniqueness and global Mittag–Leffler stability for the solutions of fractional difference model of bidirectional associative memory (BAM) neural networks. Before proceeding to the main results, we introduce the newly established discrete fractional calculus and expose some of its features. The techniques of Lyapunov function and Lyapunov direct method are then employed to prove the main results. We give two examples to verify and illustrate the theory.

Keywords: Mittag–Leffler stability, fractional difference equations, Lyapunov function, Lyapunov direct method, BAM neural networks, equilibrium point

DOI: 10.3233/JIFS-179537

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 3, pp. 2491-2501, 2020