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Keywords = fractional-order memristive cellular neural networks

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24 pages, 1057 KiB  
Article
Synchronization for Delayed Fractional-Order Memristive Neural Networks Based on Intermittent-Hold Control with Application in Secure Communication
by Xueqi Yao, Jingxi Shi, Shouming Zhong and Yuanhua Du
Fractal Fract. 2024, 8(9), 519; https://doi.org/10.3390/fractalfract8090519 - 30 Aug 2024
Cited by 1 | Viewed by 1028
Abstract
This article investigates the dynamic behaviors of delayed fractional-order memristive fuzzy cellular neural networks via the Lyapunov method. To address the delay terms of fractional-order systems, a novel lemma is provided to make the solutions of the systems exponentially stable. Furthermore, two new [...] Read more.
This article investigates the dynamic behaviors of delayed fractional-order memristive fuzzy cellular neural networks via the Lyapunov method. To address the delay terms of fractional-order systems, a novel lemma is provided to make the solutions of the systems exponentially stable. Furthermore, two new intermittent-hold controllers are designed to improve the robustness of the system and reduce the cost of the controller. One intermittent-hold controller is based on the feedback control strategy, while the other one integrates an adaptive control strategy. Moreover, two crucial theorems are derived from the proposed lemma and controllers, guaranteeing the exponential synchronization between drive and response systems. Finally, the superior performance of the controllers in achieving exponential synchronization is demonstrated through simulations. Full article
(This article belongs to the Special Issue Modeling, Optimization, and Control of Fractional-Order Neural Networks and Nonlinear Systems)
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47 pages, 1029 KiB  
Article
Brain Connectivity Dynamics and Mittag–Leffler Synchronization in Asymmetric Complex Networks for a Class of Coupled Nonlinear Fractional-Order Memristive Neural Network System with Coupling Boundary Conditions
by Aziz Belmiloudi
Axioms 2024, 13(7), 440; https://doi.org/10.3390/axioms13070440 - 28 Jun 2024
Viewed by 1390
Abstract
This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, [...] Read more.
This paper investigates the long-time behavior of fractional-order complex memristive neural networks in order to analyze the synchronization of both anatomical and functional brain networks, for predicting therapy response, and ensuring safe diagnostic and treatments of neurological disorder (such as epilepsy, Alzheimer’s disease, or Parkinson’s disease). A new mathematical brain connectivity model, taking into account the memory characteristics of neurons and their past history, the heterogeneity of brain tissue, and the local anisotropy of cell diffusion, is proposed. This developed model, which depends on topology, interactions, and local dynamics, is a set of coupled nonlinear Caputo fractional reaction–diffusion equations, in the shape of a fractional-order ODE coupled with a set of time fractional-order PDEs, interacting via an asymmetric complex network. In order to introduce into the model the connection structure between neurons (or brain regions), the graph theory, in which the discrete Laplacian matrix of the communication graph plays a fundamental role, is considered. The existence of an absorbing set in state spaces for system is discussed, and then the dissipative dynamics result, with absorbing sets, is proved. Finally, some Mittag–Leffler synchronization results are established for this complex memristive neural network under certain threshold values of coupling forces, memristive weight coefficients, and diffusion coefficients. Full article
(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
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22 pages, 1528 KiB  
Article
Finite-Time Adaptive Synchronization and Fixed-Time Synchronization of Fractional-Order Memristive Cellular Neural Networks with Time-Varying Delays
by Yihong Liu and Yeguo Sun
Mathematics 2024, 12(7), 1108; https://doi.org/10.3390/math12071108 - 7 Apr 2024
Cited by 3 | Viewed by 1287
Abstract
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the [...] Read more.
Asymptotic synchronization requires continuous external control of the system, which is unrealistic considering the cost of control. Adaptive control methods have strong robustness to uncertainties such as disturbances and unknowns. On the other hand, for finite-time synchronization, if the initial value of the system is unknown, the synchronization time of the finite-time synchronization cannot be estimated. This paper explores the finite-time adaptive synchronization (FTAS) and fixed-time synchronization (FDTS) of fractional-order memristive cellular neural networks (FMCNNs) with time-varying delays (TVD). Utilizing the properties and principles of fractional order, we introduce a novel lemma. Based on this lemma and various analysis techniques, we establish new criteria to guarantee FTAS and FDTS of FMCNNs with TVD through the implementation of a delay-dependent feedback controller and fractional-order adaptive controller. Additionally, we estimate the upper bound of the synchronization setting time. Finally, numerical simulations are conducted to confirm the validity of the finite-time and fixed-time stability theorems. Full article
(This article belongs to the Special Issue Theory, Modeling and Applications of Fractional-Order Systems)
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