scholarly journals Quasi-Synchronization of Nonidentical Fractional-Order Memristive Neural Networks via Impulsive Control

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ruihan Chen ◽  
Tianfeng Zhao
Keyword(s):  
Neural Networks ◽  
Laplace Transform ◽  
Fractional Order ◽  
Convergence Rates ◽  
Impulsive Control ◽  
Memristive Neural Networks ◽  
Impulsive Systems ◽  
The Laplace Transform ◽  
Average Impulsive Interval

This paper investigates the quasi-synchronization of nonidentical fractional-order memristive neural networks (FMNNs) via impulsive control. Based on a newly provided fractional-order impulsive systems comparison lemma, the average impulsive interval definition, and the Laplace transform, some quasi-synchronization conditions are obtained with fractional order 0 < α < 1 . In addition, the error convergence rates and error boundary are also obtained. Finally, one simulation example is presented to show the validity of our results.

scholarly journals Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 422 ◽  
Author(s):  
Grienggrai Rajchakit ◽  
Pharunyou Chanthorn ◽  
Pramet Kaewmesri ◽  
Ramalingam Sriraman ◽  
Chee Peng Lim
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Differential Inclusions ◽  
State Feedback ◽  
Control Law ◽  
Memristive Neural Networks ◽  
Numerical Examples ◽  
Quaternion Multiplication ◽  
Stabilizing Control ◽  
Stability And Stabilization

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

scholarly journals Global Synchronization of Reaction-Diffusion Fractional-Order Memristive Neural Networks with Time Delay and Unknown Parameters

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Wenjiao Sun ◽  
Guojian Ren ◽  
Yongguang Yu ◽  
Xudong Hai
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Activation Function ◽  
Memristive Neural Networks ◽  
Unknown Parameters ◽  
Global Synchronization ◽  
Adaptive Controllers ◽  
Mapping Theory

This paper investigated the global synchronization of fractional-order memristive neural networks (FMNNs). To deal with the effect of reaction-diffusion and time delay, fractional partial and comparison theorem are introduced. Based on the set value mapping theory and Filippov solution, the activation function is extended to discontinuous case. Adaptive controllers with a compensator are designed owing to the existence of unknown parameters, with the help of Gronwall–Bellman inequality. Numerical simulation examples demonstrate the availability of the theoretical results.

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