Mittag-leffler stabilization of impulsive fractional-order neural networks with continuous and distributed delays

2017 ◽  
Author(s):  
Xiaoli Ruan ◽  
Jingping Liu
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Distributed Delays

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 Dynamics of Fractional-Order Neural Networks With Discrete and Distributed Delays

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 46071-46080
Author(s):  
Lingzhi Si ◽  
Min Xiao ◽  
Guoping Jiang ◽  
Zunshui Cheng ◽  
Qiankun Song ◽  
...  
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Distributed Delays

Global Mittag–Leffler Synchronization for Impulsive Fractional-Order Neural Networks with Delays

2018 ◽  
Vol 19 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Ramziya Rifhat ◽  
Ahmadjan Muhammadhaji ◽  
Zhidong Teng
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Synchronization Problem

AbstractIn this paper, we investigate the synchronization problem of impulsive fractional-order neural networks with both time-varying and distributed delays. By using the fractional Lyapunov method and Mittag–Leffler function, some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks and one illustrative example is given to demonstrate the effectiveness of the obtained results.

scholarly journals Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 473 ◽  
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Functions ◽  
Fractional Derivatives ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Output Coupling ◽  
Synchronization Problem ◽  
Caputo Fractional Differential Equations ◽  
Derivatives Of

The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

2017 ◽  
Vol 49 (3) ◽  
pp. 537-545 ◽  
Author(s):  
Hai Zhang ◽  
Renyu Ye ◽  
Song Liu ◽  
Jinde Cao ◽  
Ahmad Alsaedi ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Distributed Delays

scholarly journals Globally projective synchronization for Caputo fractional quaternion-valued neural networks with discrete and distributed delays

2021 ◽  
Vol 6 (12) ◽  
pp. 14000-14012
Author(s):  
Chen Wang ◽  
◽  
Hai Zhang ◽  
Hongmei Zhang ◽  
Weiwei Zhang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
Fractional Order ◽  
Direct Method ◽  
Distributed Delays ◽  
Projective Synchronization ◽  
Lyapunov Direct Method ◽  
Algebraic Criterion ◽  
Inequality Techniques

<abstract><p>This paper is devoted to discussing the globally projective synchronization of Caputo fractional-order quaternion-valued neural networks (FOQVNNs) with discrete and distributed delays. Without decomposing the FOQVNNs into several subsystems, by employing the Lyapunov direct method and inequality techniques, the algebraic criterion for the globally projective synchronization is derived. The effectiveness of the proposed result is illustrated by the MATLAB toolboxes and numerical simulation.</p></abstract>

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