Synchronization for fractional-order reaction–diffusion competitive neural networks with leakage and discrete delays

2021 ◽  
Vol 436 ◽  
pp. 47-57
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Reaction Diffusion ◽  
Order Reaction ◽  
Discrete Delays

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.

Delayed Reaction–Diffusion Cellular Neural Networks of Fractional Order: Mittag–Leffler Stability and Synchronization

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Ivanka M. Stamova ◽  
Stanislav Simeonov
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Delayed Reaction

This research introduces a model of a delayed reaction–diffusion fractional neural network with time-varying delays. The Mittag–Leffler-type stability of the solutions is investigated, and new sufficient conditions are established by the use of the fractional Lyapunov method. Mittag–Leffler-type synchronization criteria are also derived. Three illustrative examples are established to exhibit the proposed sufficient conditions.

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