Article
Mathematics, Interdisciplinary Applications
Joel Perez Padron, Jose P. Perez, Jose Javier Perez Diaz, Carlos Astengo-Noguez
Summary: In this research, time-delay adaptive synchronization and adaptive anti-synchronization of chaotic fractional order systems are analyzed using the Caputo fractional derivative. The problem of synchronization and anti-synchronization of chaotic systems with variable fractional order is solved using the fractional order PID control law, adaptive laws of variable-order fractional calculus, and a control law derived from Lyapunov's theory extended to systems of time-delay variable-order fractional calculus. This research solves two important problems in the control area: synchronization of chaotic systems with adaptive fractional order and time delay using the fractional order PID control law and adaptive laws, and anti-synchronization of chaotic systems with adaptive fractional order and time delay using the fractional order PID control law and adaptive laws.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Theory & Methods
Feifei Du, Jun-Guo Lu
Summary: This paper investigates the adaptive finite-time synchronization problems for a class of fractional-order delayed fuzzy cellular neural networks (FODFCNNs). First, new perspective is provided to explore finite-time synchronization of fractional-order systems by establishing novel fractional-order differential inequalities with the aid of the properties of the Mittag-Leffler function and the Laplace transform with the parameter. Second, sufficient conditions are given based on these inequalities and the designed adaptive controller to guarantee the adaptive finite-time synchronization of FODFCNNs. Finally, the effectiveness of the results is demonstrated by a numerical example.
FUZZY SETS AND SYSTEMS
(2023)
Article
Mathematics, Interdisciplinary Applications
Kaiquan Xiang, Qiaokun Kang, Hao Chang, Jing Yang
Summary: This paper addresses the finite-time cluster synchronization issues for fractional-order fully complex-valued dynamical networks with time delay. Delay-dependent and delay-independent adaptive controllers are developed to compensate for the limited application of one controller, considering quadratic and absolute-valued norms, respectively. The paper provides detailed Lyapunov analysis based on the finite-time stability theorem and auxiliary inequality techniques to ensure that the networks can achieve finite-time cluster synchronization. Simulation examples are provided to verify the theoretical analysis.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Wenhao Yan, Zijing Jiang, Xin Huang, Qun Ding
Summary: We propose an adaptive radial basis neural network controller based on Lyapunov stability theory for uncertain fractional-order time-delay chaotic systems with different time delays. The controller achieves synchronous control without knowledge of the system model and in the presence of unknown nonlinear uncertainties and external disturbances. Stability analysis demonstrates that the error system asymptotically tends to zero in combination with a relevant lemma. Numerical simulations confirm the effectiveness of the controller.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Information Systems
Hongguang Fan, Yi Zhao
Summary: This paper investigates the adaptive cluster synchronization of fractional-order complex networks with internal and coupling delays, as well as time-varying disturbances using fractional-order hybrid controllers. The results extend previous literature by providing sufficient conditions for cluster synchronization of two kinds of fractional-order nonlinear dynamical systems. Numerical simulations confirm the effectiveness of the theoretical results.
Article
Computer Science, Artificial Intelligence
Lingzhong Zhang, Jie Zhong, Jianquan Lu
Summary: This paper investigates the finite-time synchronization problem for fractional-order complex dynamical networks with intermittent control. A general fractional-order intermittent differential inequality is obtained and criteria for finite-time convergence are established. The theoretical results are illustrated by numerical examples.
Article
Mathematics
Yi Wang, Zhaoyan Wu
Summary: This paper investigates the cluster synchronization of a variable-order fractional community network with nonidentical dynamics. Intermittent controllers are designed and sufficient conditions are derived based on stability theory of fractional-order system and LMIs. A simple corollary is provided to avoid verifying the LMIs, and a numerical example is performed to verify the result.
Article
Mathematics, Interdisciplinary Applications
Shilong Zhang, Feifei Du, Diyi Chen
Summary: This article investigates quasi-synchronization for a class of fractional-order delayed neural networks. By introducing a new fractional-order differential inequality and designing an adaptive controller, an effective criterion is proposed to ensure the quasi-synchronization.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Information Systems
Yihong Liu, Yeguo Sun, Lei Liu
Summary: This paper investigates the stability analysis and synchronization control of a fractional-order time-varying delay inertial neural network. A time-varying delay inertial neural network model is established for engineering applications. Based on the properties of the Caputo fractional derivative and the proposed lemma, the original inertial system is transformed into a conventional system and a synchronous control strategy is established. The stability conditions of a class of Caputo fractional-order time-delay inertial neural networks are provided. Simulation examples are given to verify the proposed method.
Article
Mathematics
Joel Perez Padron, Jose Paz Perez, Jose Javier Perez Diaz, Atilano Martinez Huerta
Summary: In this research paper, the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations is solved using PID control theory and Lyapunov-Krasovskii stability theory. The results obtained through simulation with examples demonstrate satisfactory outcomes in achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.
Article
Mathematics, Applied
Hongguang Fan, Jihong Zhu, Hui Wen
Summary: This paper investigates the global synchronization problems of fractional-order complex dynamical networks with uncertain inner coupling and multiple time delays. A generalized delayed comparison principle with fractional-order and impulsive effects is established to overcome the difficulties caused by various delays and uncertainties. Based on the Lyapunov stability theory and mixed impulsive control technologies, new synchronization criteria for concerned complex dynamical networks are derived. The theoretical results obtained in this paper can enhance the value of previous related works.
Article
Computer Science, Artificial Intelligence
Jia-Rui Zhang, Jun-Guo Lu, Xiao-Chuang Jin, Xing-Yu Yang
Summary: This paper investigates the asymptotic stability and synchronization of fractional-order memristive neural networks with time delays. Sufficient conditions for the asymptotic stability of a fractional-order nonlinear system are given based on the FO comparison principle and inverse Laplace transform method. Then, the sufficient conditions for the asymptotic stability and synchronization of fractional-order memristive neural networks with time delays are investigated. The results in this paper are more practical and have a wider coverage of situations compared to previous related results. The validity of the results is checked by two examples.
Article
Computer Science, Information Systems
Qiaokun Kang, Qingxi Yang, Zhilong Lin, Qintao Gan
Summary: This paper focuses on the finite-time cluster synchronization issues for a class of delayed fractional-order fully complex-valued community networks, proposing a new mathematical expression and controller design method. The feasibility and effectiveness of the results are demonstrated through simulation examples.
Article
Computer Science, Artificial Intelligence
Hong -Li Li, Jinde Cao, Cheng Hu, Long Zhang, Haijun Jiang
Summary: This paper addresses the complete synchronization problem for discrete-time fractional-order fuzzy neural networks with time-varying delays. A novel discrete-time adaptive controller with time-varying delay is proposed, and the effectiveness of the theoretical results is demonstrated through numerical examples.
Article
Mathematics, Interdisciplinary Applications
Yunzhan Bai, Juan Yu, Cheng Hu
Summary: This paper investigates the synchronization of fractional-order output-coupling multiplex networks (FOOCMNs). A type of fractional-order multiplex network is introduced, where the intra-layer and inter-layer couplings are described separately, and nodes communicate via their outputs. Sufficient conditions for achieving asymptotic synchronization are provided based on designed adaptive control, and a quantized adaptive controller is developed to improve the effective utilization rate of network resources.
FRACTAL AND FRACTIONAL
(2023)
