Global asymptotic stability of neutral type fractional‐order memristor‐based neural networks with leakage term, discrete and distributed delays

2021 ◽  
Author(s):  
M. Syed Ali ◽  
M. Hymavathi ◽  
Sumit Saroha ◽  
R. Krishna Moorthy
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Fractional Order ◽  
Global Asymptotic Stability ◽  
Neutral Type ◽  
Distributed Delays ◽  
Leakage Term

scholarly journals Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Hai Zhang ◽  
Renyu Ye ◽  
Jinde Cao ◽  
Ahmed Alsaedi
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Fractional Order ◽  
Lyapunov Functional ◽  
Equilibrium Solution ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Network Systems ◽  
Globally Asymptotic Stability ◽  
Stability Of Equilibrium

This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.

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