Improved asymptotic stability conditions for neural networks with discrete and distributed delays

2012 ◽  
Vol 89 (15) ◽  
pp. 1938-1951 ◽  
Author(s):  
Yonggang Chen ◽  
Shumin Fei ◽  
Kanjian Zhang
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Distributed Delays ◽  
Stability Conditions ◽  
Asymptotic Stability Conditions

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.

scholarly journals Existence and Global Uniform Asymptotic Stability of Pseudo Almost Periodic Solutions for Cohen-Grossberg Neural Networks with Discrete and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Hongying Zhu ◽  
Chunhua Feng
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Distributed Delays ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Uniform Asymptotic Stability ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

This paper studies the existence and uniform asymptotic stability of pseudo almost periodic solutions to Cohen-Grossberg neural networks (CGNNs) with discrete and distributed delays by applying Schauder fixed point theorem and constructing a suitable Lyapunov functional. An example is given to show the effectiveness of the main results.

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