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fixed-time synchronization of Caputo/Conformable Fractional-Order Inertial Cohen-Grossberg Neural Networks via Event-triggered One/Two-phase Hybrid Impulsive Control

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NEURAL PROCESSING LETTERS 2025年第1期57卷 1-57页

作者： Xiong, Yao Li, Yesheng Lv, Haifei Wu, Wei Xie, Songhua Chen, Mengwei Hu, Changkui Li, Min Wuhan Univ Technol Sch Sci Dept Phys Wuhan 430070 Peoples R China Wuhan Univ Sch Phys & Technol Wuhan 430072 Peoples R China Wuhan Univ Suzhou Inst Suzhou 215123 Peoples R China

This paper is concerned with the fixed-time synchronization (FXS) problems of Caputo/conformable fractional-order inertial Cohen-Grossberg neural networks (FOICGNNs) by one/two-phase hybrid impulsive control (HIC) through event-triggered update strategies. By utilizing the properties of fractional calculus, several novel inequalities regarding the fixed-time convergence of hybrid impulsive systems (HIS) are obtained. We especially discuss and compare the cases of Caputo and conformable fractional order to gain deep insight into fractional calculus. By applying the Lyapunov stability theory, two hybrid controllers, which consist of event-triggered continuous controllers and impulsive controllers, are designed to realize the FXS of FOICGNNs. It's worth pointing out that, we unprecedentedly study and compare the differences of the one-phase HIC and two-phase HIC, where a novel nonlinear impulsive controller is proposed and designed to obtain fixed-time convergence in the impulsive control phase. In addition, the exclusion of Zeno behavior is proved for the designed event-triggered strategy. Finally, several numerical examples are provided to illustrate the feasibility of the proposed control approach and the correctness of the theoretical results.

关键词： Neural network Inertial term Cohen-Grossberg Fractional order Caputo Conformable fixed-time synchronization Hybrid impulsive control One/two-phase Event-trigger

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fixed-time synchronization of kuramoto-oscillator networks with a simpler non-chattering controller

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PHYSICA SCRIPTA 2025年第2期100卷 025202-025202页

作者： Cai, Yuchen Liu, Xiaoting Yin, Xiangxin Wu, Jie Sun, Yongzheng China Univ Min & Technol Sch Math Xuzhou 221116 Peoples R China Jiangnan Univ Sch Artificial Intelligence & Comp Sci Wuxi 214122 Peoples R China

In this paper, Kuramoto-oscillator networks with identical and non-identical oscillators are studied in terms of fixed-time phase agreement and frequency synchronization. Different from traditional fixed-time controllers, we propose a simpler non-chattering controller that does not contain a sign function to overcome the chattering phenomenon. Additionally, the controller does not include a linear part, enhancing simplicity and practical convenience. The upper time bound of synchronization is estimated, and sufficient conditions for realizing fixed-time synchronization are derived using stability theory. Simulation results show the validity and correctness of our theoretical analyses. Finally, we examine the influence of control parameters on synchronization time.

关键词： kuramoto-oscillator networks fixed-time synchronization non-chattering controller

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fixed-time synchronization of Clifford-valued neural networks with D operator via aperiodic semi-intermittent control

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ADVANCES IN CONTINUOUS AND DISCRETE MODELS 2025年第1期2025卷 1-16页

作者： Wang, Pan Li, Xuechen Zheng, Qianqian Xuchang Univ Sch Sci Xuchang 461000 Peoples R China Zhongyuan Inst Sci & Technol Sch Informat Engn Xuchang 461000 Peoples R China

As Clifford-valued neural networks (CVNNs) are more versatile than real-valued, complex-valued, or quaternion-valued neural networks;it is important to study their dynamical characteristics. In this paper, the fixed-time synchronization (FTS) problem for a class of delayed CVNNs with D operator via aperiodic semi-intermittent control is studied. The proposed models are first deconstructed real-valued models since Clifford numbers cannot be multiplied commutatively. To achieve the FTS result, a new controller with aperiodic and semi-intermittent characteristics is developed. The inequality technique and analytic method are utilized to identify many essential requirements in the innovative study, which contribute to the establishment of the FTS for the systems under consideration. Specifically, the settling time is accurately forecasted and is unaffected by the initial value. To validate the correctness of the obtained results, a numerical example is shown in the interim.

关键词： fixed-time synchronization Clifford-valued neural networks D operator Aperiodic semi-intermittent control time delay

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Dynamic event-triggered fixed-time synchronization of multi-layer complex networks under denial-of-service attacks

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NONLINEAR DYNAMICS 2025年第13期113卷 16821-16835页

作者： Wu, Yongbao Wu, Tong Liu, Jian Xue, Lei Southeast Univ Sch Automat Nanjing 210096 Peoples R China

This study introduces a novel dynamic event-triggered control (ETC) strategy to address the fixed-time synchronization (FXTS) challenge in multilayer complex networks facing denial-of-service (DoS) attacks. Different from the conventional ETC schemes, the proposed ETC strategy includes a new dynamic variable that enhances its adaptability to different attack scenarios, leading to a reduction in the number of triggering instants and a more efficient utilization of computing resources. The technique of mean inactive-attack rate significantly mitigates the impacts of intermittent DoS attacks, and a novel FXTS theorem is formulated. Our findings indicate that the convergence time estimation is independent of initial values, thus eliminating Zeno behavior. Eventually, numerical simulations involving Chua's circuit further validate the practicality and robustness of the proposed theoretical framework.

关键词： Denial-of-service attacks Event-triggered control fixed-time synchronization Mean inactive-attack rate Multilayer complex networks

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Impulsive effects on delayed fractional-order neural networks: sliding mode control-based fixed-time synchronization analysis

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NONLINEAR DYNAMICS 2025年第13期113卷 16571-16592页

作者： Cheng, Yali Yang, Wanying Xu, Wenbo Zhong, Shouming Univ Elect Sci & Technol China Sch Resources & Environm Chengdu Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu Peoples R China

This paper included a detailed discussion of the delayed fractional-order neural networks (FONNs) subject to impulse effects as well as their fixed-time synchronization (FXTS) problem. To explore this issue, an advanced fixed-time stability (FTS) is introduced, which considers the impact of order alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} on settling-time (ST), allows time-varying functions for the coefficients and indefinite derivatives of the Lyapunov function (LF). Next, several measures are adopted to handle issues in control systems. Firstly, a piecewise function is utilized within the integral function to avoid integral windup. Secondly, a class of fractional-order integral sliding mode control (FOSMC) and a class of fractional-order integral sliding mode surface (FOSMS) with odd power characteristics are designed. This design addresses the chattering problem resulting from the sign function and enables the fixed-time reachability and stability of the sliding mode dynamics. Subsequently, several relevant conditions were obtained to solve the FXTS problem of FONNs with impulse effects. At last, to verify the effectiveness of the theoretical results, a numerical simulation is provided.

关键词： Fractional-order neural networks fixed-time synchronization fixed-time stability Sliding mode control Impulsive effects

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Improved results on fixed-time synchronization of complex-valued fuzzy BAM neural networks with random impulsive effects

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INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL 2025年第4期13卷 1-18页

作者： Tohti, Rukeya Abdurahman, Abdujelil Xinjiang Univ Coll Math & Syst Sci Urumqi 830046 Xinjiang Peoples R China

This paper investigates the fixed-time (FxT) stability of nonlinear impulsive systems and the FxT synchronization of complex-valued fuzzy binary association memory neural networks (BAM-NNs) with random impulsive effects. Firstly, some improved and easily applicable FxT stability results are introduced for a type of impulsive nonlinear systems which incorporates both stabilizing and destabilizing impulsive effects. Then, the established FxT stability results are employed to investigate the FxT synchronization of fuzzy BAM-NNs on complex domain with general impulsive effects under the simple nonlinear controller which only consists of two nonlinear terms. Compared with the recent published studies, the estimation accuracy of settling time is refined by assessing the value of an improper integral more accurately. Finally, two examples are presented to substantiate the validity of our obtained results.

关键词： fixed-time synchronization Complex-valued neural network Hybrid impulse Fuzzy BAM neural network

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fixed-time synchronization of proportional delay memristive complex-valued competitive neural networks

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NEURAL NETWORKS 2025年 188卷 107411页

作者： Han, Jiapeng Zhou, Liqun Tianjin Normal Univ Sch Math Sci Tianjin 300387 Peoples R China Tianjin Normal Univ Inst Math & Interdisciplinary Sci Tianjin 300387 Peoples R China

The fixed-time synchronization (FXS) is considered for memristive complex-valued competitive neural networks (MCVCNNs) with proportional delays. Two less conservative criteria supporting the FXS of MCVCNNs are founded by involving Lyapunov method and inequality techniques. Suitable switch controllers are designed by defining different norms of complex numbers instead of treating complex-valued neural networks as two real-valued systems. Furthermore, the settling time (ST) has been approximated. Finally, two simulations are shown to confirm the effectiveness of criteria in this paper and the outcomes of practical application in image protection.

关键词： fixed-time synchronization Competitive neural networks Proportional delays Complex-valued neural networks

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fixed-time synchronization of discontinuous complex-valued BAM neural networks with time delays

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NEUROCOMPUTING 2025年 638卷

作者： Wang, Qian Qian, Yinjie Qiao, Yuanhua Changsha Univ Sci & Technol Sch Math & Stat Changsha 410114 Hunan Peoples R China Beijing Univ Technol Sch Math Stat & Mech Beijing 100124 Peoples R China

The fixed-time synchronization (FTS) of discontinuous complex-valued bidirectional associative memory neural networks (CVBAMNNs) with time delays is investigated in this paper. First, CVBAMNNs are separated into real and imaginary parts, the equivalent real-valued subsystems are constructed for the analysis. Then, two kinds of discontinuous feedback controllers are designed, and two forms of Lyapunov function based on p-norm and 1-norm are constructed to study the FTS of CVBAMNNs. By using differential inclusions theory and some inequality techniques, some neoteric criteria are established to achieve FTS, and the upper-bound of the setting time is more explicitly estimated as well. Finally, numerical simulations are presented to verify the effectiveness and applicability of the developed theoretical results.

关键词： Complex-valued BAM neural network Discontinuous activation fixed-time synchronization

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Aperiodically semi-intermittent-based fixed-time stabilization and synchronization of delayed discontinuous inertial neural networks

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Science China(Information Sciences) 2025年第1期68卷 238-254页

作者： Guodong ZHANG Jinde CAO School of Mathematics and Statistics South-Central Minzu University School of Mathematics Southeast University

This article concentrates on the fixed-time stabilization(FS) and fixed-time synchronization(FTS) of discontinuous inertial neural networks(DINNs) with distributed delays. Using mathematical induction to a new differential equality, a novel fixed-time stability lemma is constructed. Then, by designing an aperiodically semi-intermittent switching control and combining it with the theory of nonsmooth analysis, some novel criteria on the FS and FTS of DINNs are obtained. Unlike the methods used in most existing studies, the FS and FTS results are structured using the newly proposed fixed-time stability lemma and the nonreduced-order approach, resulting in broader practical applications and strengthening the scientific quality of the derived results. Lastly, numerical simulations and applications proffer the effectiveness of the established FS and FTS criteria.

关键词： inertial neural networks fixed-time synchronization semi-intermittent switching control nonreduced-order approach fixed-time stabilization

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fixed/Predefined time synchronization of fractional quaternion delayed neural networks with disturbances

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MATHEMATICS AND COMPUTERS IN SIMULATION 2025年 232卷 276-294页

作者： Zhang, Hai Gao, Panqing Ye, Renyu Stamova, Ivanka Cao, Jinde Anqing Normal Univ Sch Math & Phys Anqing 246133 Peoples R China Anqing Normal Univ Key Lab Modeling Simulat & Control Complex Ecosyst Anhui Higher Educ Inst Anqing 246133 Peoples R China Univ Texas San Antonio Dept Math San Antonio TX 78249 USA Southeast Univ Sch Math Nanjing 211189 Peoples R China

The fixed time synchronization (Fix-TS) and predefined time synchronization (Pre-TS) of fractional quaternion delayed neural networks (FQDNNs) with disturbances using fractional sliding mode (FSM) control are investigated. We first introduce an enhanced lemma for fixed time (Fix-T) and predefined time (Pre-T) stability, expanding upon the existing stability theory. Subsequently, we introduce the FQDNNs model with disturbance terms, which is less conservative. By constructing two FSM controllers, we derive several theorems for Fix-TS and Pre-TS, respectively. The concise criterion and accurate setting time are demonstrated through numerical simulations, and graphic visualization directly verifies the results.

关键词： fixed-time synchronization Predefined-time synchronization Fractional quaternion neural network Fractional sliding mode controller

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