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>

scholarly journals Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Chong Chen ◽  
Zhixia Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Direct Method ◽  
Projective Synchronization ◽  
Sliding Mode Controller ◽  
Memristive Neural Networks ◽  
Lyapunov Direct Method ◽  
Sliding Motion ◽  
Fractional Order Integral

This paper investigates projective synchronization of nonidentical fractional-order memristive neural networks (NFMNN) via sliding mode controller. Firstly, based on the sliding mode control theory, a new fractional-order integral sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, according to fractional-order differential inequalities and fractional-order Lyapunov direct method, the trajectories of the system converge to the sliding mode surface to carry out sliding mode motion, and some sufficient criteria are obtained to achieve global projective synchronization of NFMNN. In addition, the conclusions extend and improve some previous works on the synchronization of fractional-order memristive neural networks (FMNN). Finally, a simulation example is given to verify the effectiveness and correctness of the obtained results.

Global stabilization of memristor-based fractional-order neural networks with delay via output-feedback control

2017 ◽  
Vol 31 (05) ◽  
pp. 1750031 ◽  
Author(s):  
Jiyang Chen ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Xujun Yang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Output Feedback ◽  
Differential Inclusions ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Global Stabilization ◽  
Lyapunov Direct Method ◽  
Stabilizing Control

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.

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.

Adaptive impulsive synchronization for a class of fractional order complex chaotic systems

2019 ◽  
Vol 25 (10) ◽  
pp. 1614-1628 ◽  
Author(s):  
Xingpeng Zhang ◽  
Dong Li ◽  
Xiaohong Zhang
Keyword(s):  
Number Field ◽  
Fractional Order ◽  
Complex Number ◽  
Chaotic Systems ◽  
Direct Method ◽  
Order Complex ◽  
Lyapunov Direct Method ◽  
Impulsive Synchronization ◽  
Complex Chaotic Systems ◽  
Order Extension

In this paper, a new lemma is proposed to study the stability of a fractional order complex chaotic system without dividing the complex number into real and imaginary parts. The proving process of the new lemma combines the fundamental properties of the complex field and the fractional order extension of the Lyapunov direct method. It extends the fractional order extension of the Lyapunov direct method from the real number field to the complex number field. Based on the new lemma, we propose a new impulsive synchronization scheme for fractional order complex chaotic systems. The numerical simulation results also show the validity of our conclusion.

Improved Control Schemes for Projective Synchronization of Delayed Neural Networks with Unmatched Coefficients

2019 ◽  
Vol 34 (03) ◽  
pp. 2051005 ◽  
Author(s):  
Abdujelil Abdurahman ◽  
Haijun Jiang
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Chaos Synchronization ◽  
Projective Synchronization ◽  
Chaotic Neural Networks ◽  
Delayed Neural Networks ◽  
Mixed Time Delays ◽  
Control Schemes ◽  
Master System ◽  
Inequality Techniques

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper.

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