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Keywords = global Mittag-Leffler synchronization

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25 pages, 2044 KB  
Article
Global Mittag-Leffler Synchronization of Fractional-Order Fuzzy Inertia Neural Networks with Reaction–Diffusion Terms Under Boundary Control
by Lianyang Hu, Haijun Jiang, Cheng Hu, Yue Ren, Lvming Liu and Xuejiao Qin
Fractal Fract. 2025, 9(7), 405; https://doi.org/10.3390/fractalfract9070405 - 23 Jun 2025
Cited by 1 | Viewed by 925
Abstract
This study is devoted to solving the global Mittag-Leffler synchronization problem of fractional-order fuzzy reaction–diffusion inertial neural networks by using boundary control. Firstly, the considered network model incorporates the inertia term, reaction–diffusion term and fuzzy logic, thereby enhancing the existing model framework. Secondly, [...] Read more.
This study is devoted to solving the global Mittag-Leffler synchronization problem of fractional-order fuzzy reaction–diffusion inertial neural networks by using boundary control. Firstly, the considered network model incorporates the inertia term, reaction–diffusion term and fuzzy logic, thereby enhancing the existing model framework. Secondly, to prevent an increase in the number of state variables due to the reduced-order approach, a non-reduced-order method is fully utilized. Additionally, a boundary controller is designed to lower resource usage. Subsequently, under the Neumann boundary condition, the mixed boundary condition and the Robin boundary condition, three synchronization conditions are established with the help of the non-reduced-order approach and LMI technique, respectively. Lastly, two numerical examples are offered to verify the reliability of the theoretical results and the availability of the boundary controller through MATLAB simulations. Full article
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24 pages, 1296 KB  
Article
Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers
by M. Syed Ali, Gani Stamov, Ivanka Stamova, Tarek F. Ibrahim, Arafa A. Dawood and Fathea M. Osman Birkea
Mathematics 2023, 11(20), 4248; https://doi.org/10.3390/math11204248 - 11 Oct 2023
Cited by 6 | Viewed by 1622
Abstract
In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The [...] Read more.
In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results. Full article
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20 pages, 549 KB  
Article
Synchronization of Discrete-Time Fractional-Order Complex-Valued Neural Networks with Distributed Delays
by R. Perumal, M. Hymavathi, M. Syed Ali, Batul A. A. Mahmoud, Waleed M. Osman and Tarek F. Ibrahim
Fractal Fract. 2023, 7(6), 452; https://doi.org/10.3390/fractalfract7060452 - 1 Jun 2023
Cited by 4 | Viewed by 2008
Abstract
This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete [...] Read more.
This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov’s direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples. Full article
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13 pages, 1862 KB  
Article
Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System
by Xinggui Li, Ruofeng Rao, Shouming Zhong, Xinsong Yang, Hu Li and Yulin Zhang
Mathematics 2022, 10(15), 2737; https://doi.org/10.3390/math10152737 - 2 Aug 2022
Cited by 13 | Viewed by 1929
Abstract
This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can [...] Read more.
This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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12 pages, 286 KB  
Article
Impulsive Memristive Cohen–Grossberg Neural Networks Modeled by Short Term Generalized Proportional Caputo Fractional Derivative and Synchronization Analysis
by Ravi Agarwal and Snezhana Hristova
Mathematics 2022, 10(13), 2355; https://doi.org/10.3390/math10132355 - 5 Jul 2022
Cited by 6 | Viewed by 1914
Abstract
The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when the control input is acting continuously as well as when it is [...] Read more.
The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when the control input is acting continuously as well as when it is acting instantaneously at the impulsive times. We defined the global Mittag–Leffler synchronization as a generalization of exponential synchronization. We obtained some sufficient conditions for Mittag–Leffler synchronization. Our results are illustrated with examples. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
20 pages, 314 KB  
Article
Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays
by Ravi Agarwal, Snezhana Hristova and Donal O’Regan
Symmetry 2018, 10(10), 473; https://doi.org/10.3390/sym10100473 - 10 Oct 2018
Cited by 13 | Viewed by 3009
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fractional Differential Equations: Theory, Methods and Applications)
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