Asymptotic stability and synchronization of fractional order Hopfield neural networks with unbounded delay

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$Asymptotic stability and synchronization of fractional order Hopfield neural networks with unbounded delay$

Asymptotic stability and synchronization of fractional order Hopfield neural networks with unbounded delay

He, Bin‐bin; Zhou, Hua‐Cheng

Mathematical methods in the applied sciences, February 2023, Volume: 46, Issue: 3

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In this paper, the asymptotic stability and synchronization of fractional order Hopfield neural networks (FOHNNs) with time‐varying delay are investigated. First, we propose an extended fractional Halanay inequality, which plays an essential role in the proof of the main results. Using the Banach fixed point theorem, the existence and uniqueness of the equilibrium point of the system is proved. Through the extended Halanay inequality and a useful fractional derivative inequality, the sufficient conditions of the asymptotic stability and synchronization are given for FOHNNs. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.

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