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projective synchronization for distinct fractional-order neural networks consist of inconsistent orders via sliding mode control

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2024年 133卷

作者： Zhou, Junshuang Li, Deyi Chen, Guici Wen, Shiping Wuhan Univ Sci & Technol Coll Sci Wuhan 430065 Peoples R China Wuhan Univ Sci & Technol Hubei Prov Key Lab Syst Sci Met Proc Wuhan 430065 Peoples R China Univ Technol Sydney Ctr Artificial Intelligence Sydney 2007 Australia

The present study delves into the projective synchronization for distinct fractional-order neural networks consist of inconsistent orders, employing the principles of sliding mode control and incorporating fractional operators within the controller. Firstly, incorporating the fractionalorder derivative into the controller facilitates the derivation of a synchronous error system, and a well-suited integral-type sliding switching surface is subsequently constructed, along with the development of an appropriate sliding mode controller, thereby ensuring the existence of sliding movement derived from the principle of sliding mode control. Then through the application of the Lyapunov direct method, it is shown that the sliding mode controller steers the evolution of error system towards the designated sliding switching surface and maintains therein indefinitely, meanwhile, novel criteria for achieving projective synchronization for distinct fractional-order neural networks consist of inconsistent orders is established. Lastly, to exemplify the efficacy and practical applications of the proposed approach, simulations with two types of distinct fractional-order neural networks are carried out utilizing a continuous frequency distribution model.

关键词： projective synchronization Distinct drive-response system Inconsistent orders Fractional-order derivative sliding mode controller

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projective synchronization for quaternion-valued memristor-based neural networks under time-varying delays

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NETWORKS AND HETEROGENEOUS MEDIA 2024年第3期19卷 1156-1181页

作者： Guo, Jun Shi, Yanchao Cheng, Yanzhao Luo, Weihua Chengdu Univ Informat Technol Coll Appl Math Chengdu 610225 Peoples R China Neijiang Normal Univ Key Lab Numer Simulat Sichuan Prov Univ Sch Math & Informat Sci Neijiang 641000 Peoples R China Southwest Petr Univ Sch Sci Chengdu 610500 Peoples R China Hunan Univ Arts & Sci Sch Math & Phys Changde 415000 Peoples R China

In this paper, the projective synchronization of quaternion-valued memristor-based neural networks with time-varing delays was studied. First, by utilizing set-valued map and differential inclusion theories, we reformulated the networks as an uncertain system with interval parameters. Then, through designing a novel controller and utilizing Lyapunov function and Young's inequality, several new synchronization conditions for projection synchronization of quaternion-valued memristor-based neural networks were obtained. Finally, the effectiveness of this method was demonstrated through a numerical example, underscoring its practical applicability.

关键词： projective synchronization quaternion-valued time-varying delays memristor-based neural networks

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projective synchronization of Inertial Quaternion-Valued Neural Networks via Non-reduced Order Approach

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NEURAL PROCESSING LETTERS 2024年第1期56卷 21-21页

作者： Huang, Qun Yu, Yue Cao, Jinde Nantong Univ Sch Math & Stat Nantong 226019 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China

In this article, the issue on projective synchronization of delayed inertial quaternion-valued neural networks (IQVNNs) is investigated. Different from most existing literature, we adopt the non-reduced order approach to deal with IQVNNs described by second order differential equations. By introducing a novel Lyapunov functional, several sufficient criteria are presented in component form to ensure the projective synchronization between master-slave systems. A numerical experiment demonstrates the feasibility of control strategy as well as the correctness of theoretical results.

关键词： projective synchronization Quaternion-valued neural networks Inertial term Non-reduced order approach

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projective synchronization for Uncertain Fractional Reaction-Diffusion Systems via Adaptive Sliding Mode Control Based on Finite-Time Scheme

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第11期35卷 15638-15646页

作者： Kao, Yonggui Cao, Yue Chen, Yangquan Harbin Inst Technol Dept Math Weihai 264209 Peoples R China Univ Calif Merced Sch Engn Dept Mechatron Embedded Syst & Automat Merced CA 95343 USA

In this article, the projective synchronization of uncertain fractional-order (FO) reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control (SMC) method. A FO integral type switching function is designed, and corresponding adaptive SMC laws are derived which ensure the FO sliding mode surface (SMS) is reachable after a finite time interval. The improved version of these control laws which have smaller oscillation and better control performance are also derived. A new lemma for proving the finite-time reachability of the FO SMS is developed. At last, numerical examples are provided to verify the effectiveness of our theories.

关键词： synchronization Artificial neural networks Adaptive control Uncertainty Switches Power system stability Boundary conditions Adaptive control finite time fractional reaction-diffusion system projective synchronization sliding mode control (SMC)

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projective synchronization of a nonautonomous delayed neural networks with Caputo derivative

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International Journal of Biomathematics 2024年第7期17卷 241-272页

作者： Changyou Wang Zongxin Lei Lili Jia Yuanhua Du Qiuyan Zhang Jun Liu College of Applied Mathematics Chengdu University of Information Technology Chengdu 610225P.R.China Dianchi College of Yunnan University Kunming Yunnan 650228P.R.China School of Mathematical Sciences Sichuan Normal University Chengdu 610066P.R.China School of Automation Chengdu University of Information Technology Chengdu 610225P.R.China

In this paper,the projective synchronization problem of nonautonomous neural networks with time delay and Caputo derivative is ***,by introducing time delay and variable coefficient into the known neural network model,the neural network that can more accurately describe the interaction between neurons is ***,based on the improved neural network model,two global synchronization schemes are achieved,***,by constructing two novel Lyapunov functions and utilizing the properties of delay fractional-order differential inequalities,the asymptotic stability of the zero equilibrium point of the error system obtained from the master-slave systems is proved by some new developing analysis methods,respectively,and some criteria for global projective synchronization of delayed nonautonomous neural networks with Caputo derivatives are obtained,respectively,under two new synchronous *** addition,the correctness of the theoretical results obtained in this paper is verified by some numerical simulation.

关键词： Time delay Caputo derivative nonautonomous neural network projective synchronization

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projective synchronization of fractional-order quaternion-valued neural networks with Mittag-Leffler kernel

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INTERNATIONAL JOURNAL OF GENERAL SYSTEMS 2025年

作者： Ansari, Md Samshad Hussain Malik, Muslim Nieto, Juan J. Indian Inst Technol Mandi Sch Math & Stat Sci Mandi India Univ Santiago De Compostela Dept Stat Math Anal & Optimizat CITMAGA Santiago De Compostela Spain

We consider fractional-order quaternion-valued neural networks (FO-QVNNs) with Mittag-Leffler kernel and study projective synchronization. We establish Mittag-Leffler projective synchronization (MLPS) and asymptotic projective synchronization for the FO-QVNNs. Initially, a novel fractional differential inequality for the fractional derivative is established to study the synchronization of fractional-order systems. Subsequently, quaternion-valued feedback controllers are designed. Conditions for MLPS are then formulated using quaternion techniques, the proposed inequality and the properties of fractional calculus. The effectiveness and practicality of the proposed methodologies are displayed through numerical simulations in a concrete case.

关键词： Mittag-Leffler function fractional derivative quaternion-valued neural networks projective synchronization

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projective synchronization results of fractional order quaternion valued neural networks with proportional delay under event-triggered control

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 282卷

作者： He, Yan Zhang, Weiwei Zhang, Hai Cao, Jinde Abdel-Aty, Mahmoud Anqing Normal Univ Sch Math & Phys Anqing 246133 Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 210093 Peoples R China Anqing Normal Univ Key Lab Modeling Simulat & Control Complex Ecosyst Anqing 246133 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Jadara Univ Jadara Res Ctr Irbid 21110 Jordan Ahlia Univ Deanship Grad Studies & Res Manama Bahrain

This paper explores the projective synchronization (PS) of fractional order neural networks (FONNs) with proportional delay in quaternion through non-decomposition method. A controller with proportional delay is designed from the perspective of reducing the times of controller updates and computational costs, and corresponding event-triggered conditions are provided. The criteria for achieving PS of the systems are obtained through techniques such as mean value inequality and Razumikhin's theorem. On the basis of this derivation, the conditions for systems to achieve PS are explored when two consecutive releases are fixed. In addition, the positive lower bound of the inter-event time is derived, Zeno behavior can be excluded. Finally, the validity of the theoretical results is obtained through simulation. Additionally, the application of the system studied in this paper in image encryption and decryption is presented.

关键词： Proportional delay Quaternion-valued projective synchronization Event triggered Zeno behavior

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projective synchronization of fractional order quaternion valued uncertain neural networks

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CHINESE JOURNAL OF PHYSICS 2024年 88卷 740-755页

作者： Ansari, Md Samshad Hussain Malik, Muslim Indian Inst Technol Sch Math & Stat Sci Mandi 175005 Himachal Prades India

In this manuscript, we investigate the projective synchronization (PS) of fractional -order quaternion-valued uncertain competitive neural networks (FQVUCNNs). First, we construct quaternion-valued adaptive control and use this control to ensure the realization of asymptotic adaptive projective synchronization (AAPS) for FQVUCNNs. Also, we examine finite -time projective synchronization (FTPS) of the FQVUCNNs using quaternion-valued feedback control. Instead of using the usual decomposition technique, we treat the quaternion-valued state as a single entity and establish the synchronization criteria for FQVUCNNs using the Lyapunov direct method and the properties of fractional derivatives. Further, the practical viability and effectiveness of the theoretical findings are demonstrated through an illustrative example, underlying the significance of this research.

关键词： Fractional competitive neural networks projective synchronization Quaternion Uncertainty

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projective synchronization for a new class of chaotic/hyperchaotic systems with and without parametric uncertainty

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2023年第10期45卷 1975-1985页

作者： Yadav, Nisha Pallav, Himesh Handa, Himesh Natl Inst Technol Hamirpur Dept Elect Engn Hamirpur India Natl Inst Technol Hamirpur Dept Elect Engn Hamirpur 177005 Himachal Prades India

The term "chaotic system" refers to a kind of dynamical system that is characterized by its extreme sensitivity to its initial conditions. The ability of such dynamical systems to maintain synchronization is one of the extremely crucial features of these systems. There is an increasing fascination in chaotic systems with real-state variables, and they are being discovered as well as explored in greater depth in a variety of areas of nonlinear science. In this manuscript, a mixture of active nonlinear control scheme as well as adaptive control scheme has been recommended to investigate the full-order and reduced-order projective synchronization for a unique class of chaotic and hyperchaotic systems with as well as without uncertain parameters. Active nonlinear control technique is an effective method, which has been extensively used to synchronize two chaotic systems in master-slave configuration when parameters of the systems under consideration are fully known in advance. However, in practical scenarios, system parameters are not exactly known in advance. This often occurs due to the factors such as limitations associated with the experimental conditions, mutual interference among system components or due to the influence of external environmental factors. Therefore, in such cases, the designer has to go for the adaptive control technique to develop the adaptation control laws for unknown system parameters. Adaptive active nonlinear controller and parameter adaptation laws have been introduced here using Lyapunov stability criteria to confirm that the error dynamics of the synchronizing chaotic systems become asymptotic stable. Furthermore, numerical simulations on Lorenz hyperchaotic fourth-order system and Pehlivan chaotic third-order system are shown to demonstrate that the proposed synchronization scheme is working effectively.

关键词： Active nonlinear control adaptive control full order reduced order Lyapunov stability projective synchronization unknown parameters hyperchaotic system

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projective synchronization of Discrete-Time Variable-Order Fractional Neural Networks With Time-Varying Delays

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2025年第5期36卷 9313-9325页

作者： Li, Dan-Dan Li, Hong-Li Hu, Cheng Jiang, Haijun Cao, Jinde Xinjiang Univ Coll Math & Syst Sci Urumqi 830017 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Yonsei Univ Yonsei Frontier Lab Seoul 03722 South Korea

This article is committed to studying projective synchronization and complete synchronization (CS) issues for one kind of discrete-time variable-order fractional neural networks (DVFNNs) with time-varying delays. First, two new variable-order fractional (VF) inequalities are built by relying on nabla Laplace transform and some properties of Mittag-Leffler function, which are extensions of constant-order fractional (CF) inequalities. Moreover, the VF Halanay inequality in discrete-time sense is strictly proved. Subsequently, some sufficient projective synchronization and CS criteria are derived by virtue of VF inequalities and hybrid controllers. Finally, we exploit numerical simulation examples to verify the validity of the derived results, and a practical application of the obtained results in image encryption is also discussed.

关键词： Discrete-time projective synchronization time-varying delays variable-order fractional (VF) neural networks (NNs) Discrete-time projective synchronization time-varying delays variable-order fractional (VF) neural networks (NNs)

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