Stability analysis of stochastic fractional-order competitive neural networks with leakage delay

M. Syed Ali; M. Hymavathi; Bandana Priya; Syeda Asma Kauser; Ganesh Kumar Thakur; M. Syed Ali; M. Hymavathi; Bandana Priya; Syeda Asma Kauser; Ganesh Kumar Thakur

doi:10.3934/math.2021193

AIMS Mathematics

2021, Volume 6, Issue 4: 3205-3241. doi: 10.3934/math.2021193

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Stability analysis of stochastic fractional-order competitive neural networks with leakage delay

1.
Department of Mathematics, Thiruvalluvar University, Vellore - 632 115, Tamilnadu, India
2.
Department of Applied Sciences, G L Bajaj Institute of Technology and Management, Greater Noida, India
3.
Department of Mathematics, Prince sattam bin Abdulaziz University, Kingdom of Saudi Arabia
4.
Department of Applied Sciences, Krishna Engineering College, Ghaziabad, Uttar Pradesh, India

Received: 04 October 2020 Accepted: 31 December 2020 Published: 15 January 2021
MSC : 93D05

This article, we explore the stability analysis of stochastic fractional-order competitive neural networks with leakage delay. The main objective of this paper is to establish a new set of sufficient conditions, which is for the uniform stability in mean square of such stochastic fractional-order neural networks with leakage. Specifically, the presence and uniqueness of arrangements and stability in mean square for a class of stochastic fractional-order neural systems with delays are concentrated by using Cauchy-Schwartz inequality, Burkholder-Davis-Gundy inequality, Banach fixed point principle and stochastic analysis theory, respectively. Finally, four numerical recreations are given to confirm the hypothetical discoveries.
- fractional order,
- stochastic,
- competitive neural networks,
- leakage
Citation: M. Syed Ali, M. Hymavathi, Bandana Priya, Syeda Asma Kauser, Ganesh Kumar Thakur. Stability analysis of stochastic fractional-order competitive neural networks with leakage delay[J]. AIMS Mathematics, 2021, 6(4): 3205-3241. doi: 10.3934/math.2021193

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Abstract

This article, we explore the stability analysis of stochastic fractional-order competitive neural networks with leakage delay. The main objective of this paper is to establish a new set of sufficient conditions, which is for the uniform stability in mean square of such stochastic fractional-order neural networks with leakage. Specifically, the presence and uniqueness of arrangements and stability in mean square for a class of stochastic fractional-order neural systems with delays are concentrated by using Cauchy-Schwartz inequality, Burkholder-Davis-Gundy inequality, Banach fixed point principle and stochastic analysis theory, respectively. Finally, four numerical recreations are given to confirm the hypothetical discoveries.

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