Dynamic analysis of fractional-order neural networks with inertia

Zhiying Li; Wangdong Jiang; Yuehong Zhang; Zhiying Li; Wangdong Jiang; Yuehong Zhang

doi:10.3934/math.2022927

AIMS Mathematics

2022, Volume 7, Issue 9: 16889-16906. doi: 10.3934/math.2022927

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Research article

Dynamic analysis of fractional-order neural networks with inertia

The Fundamental Education Department of Yuanpei College, Shaoxing University, Shaoxing 312000, China

Received: 23 May 2022 Revised: 28 June 2022 Accepted: 01 July 2022 Published: 15 July 2022
MSC : 45M05

The existence and the S-asymptotic $ \omega $-periodic of the solution in fractional-order Cohen-Grossberg neural networks with inertia are studied in this paper. Based on the properties of the Riemann-Liouville (R-L) fractional-order derivative and integral, the contraction mapping principle, and the Arzela-Ascoli theorem, sufficient conditions for the existence and the S-asymptotic $ \omega $-period of the system are achieved. In addition, an example is simulated to testify the theorem.
- fractional-order neural networks,
- contraction mapping principle,
- inertia,
- existence,
- S-asymptotic $ \omega $-periodic
Citation: Zhiying Li, Wangdong Jiang, Yuehong Zhang. Dynamic analysis of fractional-order neural networks with inertia[J]. AIMS Mathematics, 2022, 7(9): 16889-16906. doi: 10.3934/math.2022927

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Abstract

The existence and the S-asymptotic $ \omega $-periodic of the solution in fractional-order Cohen-Grossberg neural networks with inertia are studied in this paper. Based on the properties of the Riemann-Liouville (R-L) fractional-order derivative and integral, the contraction mapping principle, and the Arzela-Ascoli theorem, sufficient conditions for the existence and the S-asymptotic $ \omega $-period of the system are achieved. In addition, an example is simulated to testify the theorem.

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