具有未知参数的两个混沌系统组的固定时间函数组合同步

李德奎; 魏兴民; 吴建军

doi:10.1051/wujns/2026315471

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具有未知参数的两个混沌系统组的固定时间函数组合同步

Mathematics | 更新时间：2026-10-29

- 具有未知参数的两个混沌系统组的固定时间函数组合同步
- Fixed-Time Function Combination Synchronization of the Two Chaotic System Groups with Unknown Parameters
- 武汉大学学报自然科学英文版 2026年31卷第5期页码：471-480
- 作者机构：
  
  甘肃中医药大学公共卫生学院, 甘肃兰州 730101
- 作者简介：
  
  LI Dekui, male, Professor, research direction: theory and apply of chaotic system. E-mail: dkli2009@163.com
- 基金信息：
  
  the National Natural Science Foundation of China(11161027);the Gansu Province Disease Prevention and Control Scientific Research Project(GSJKKY-2025-10)
- DOI：10.1051/wujns/2026315471
  中图分类号： TP273
- 收稿：2025-03-17，
  
  纸质出版：2026-10-24
- 稿件说明：
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李德奎,魏兴民,吴建军.具有未知参数的两个混沌系统组的固定时间函数组合同步[J].武汉大学学报自然科学英文版,2026,31(05):471-480.

LI Dekui, WEI Xingmin, WU Jianjun. Fixed-Time Function Combination Synchronization of the Two Chaotic System Groups with Unknown Parameters[J]. ,Wuhan Univ J of Nat Sci, 2026, 31(5): 471-480.
李德奎,魏兴民,吴建军.具有未知参数的两个混沌系统组的固定时间函数组合同步[J].武汉大学学报自然科学英文版,2026,31(05):471-480. DOI： 10.1051/wujns/2026315471.

LI Dekui, WEI Xingmin, WU Jianjun. Fixed-Time Function Combination Synchronization of the Two Chaotic System Groups with Unknown Parameters[J]. ,Wuhan Univ J of Nat Sci, 2026, 31(5): 471-480. DOI： 10.1051/wujns/2026315471.

摘要

本文提出并研究了具有未知参数的两个混沌系统组的固定时间函数组合同步

其中一个系统组称为驱动系统组

由

个不同的混沌系统组成

另一个由

个不同的混沌系统组成的系统组称为响应系统组。根据李雅普诺夫稳定性定理和自适应控制技术

设计一个自适应控制器

实现两个系统组的同步。虽然响应系统组中有很多个响应系统

但是只需控制其中任何一个响应系统

就能实现两个系统组的这种同步。同时

设计的参数辨识法则能够准确辨识所有的未知参数

同步时间不依赖于系统的初值。给出的一

些数值实例证明了所得结论的正确性。

Abstract

In this paper

fixed-time function combination synchronization of two system groups with unknown parameters is proposed and studied

where one system group is called the drive system group made up of

different chaotic systems

and the other system group made up by

different chaotic systems is called the response system group. According to Lyapunov theorem and adaptive control technology

we devise an adaptive controller to achieve the synchronization of the two system groups. Although there are many response systems

the synchronization of the two system groups can be realized by controlling only one response system. At the same time

the designed parameter identification laws can identify accurately all the unknown parameters. The synchronization time does not rely on initial values of all the systems. Some numerical examples are given to prove the correctness of the conclusions.

关键词

Keywords

references

Pecora L M , Carroll T L . Synchronization in chaotic systems [J ] . Physical Review Letters , 1990 , 64 ( 8 ): 821 - 824 .

Zhang C L , Li J M . Hybrid function projective synchronization of chaotic systems with uncertain time-varying parameters via Fourier series expansion [J ] . International Journal of Automation and Computing , 2012 , 9 ( 4 ): 388 - 394 .

Luo C , Wang X Y . Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification [J ] . Journal of the Franklin Institute , 2013 , 350 ( 9 ): 2646 - 2663 .

Li D K . Finite-time and fixed-time hybrid function projection synchronization of chaotic systems with unknown parameters [J ] . Journal of Lanzhou University (Natural Sciences) , 2023 , 59 ( 4 ): 512 - 523 (Ch) .

Wang H , Ye J M , Miao Z H , et al . Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication [J ] . Transactions of the Institute of Measurement and Control , 2018 , 40 ( 4 ): 1177 - 1187 .

Zhang W L , Yang T . Finite-time synchronization of discontinuous network systems via two control schemes [J ] . Franklin Open , 2024 , 6 : 100068 .

Zhang L Z , Zhong J , Lu J Q . Intermittent control for finite-time synchronization of fractional-order complex networks [J ] . Neural Networks , 2021 , 144 : 11 - 20 .

Chen C , Li L X , Peng H P , et al . Fixed-time synchronization of inertial memristor-based neural networks with discrete delay [J ] . Neural Networks , 2019 , 109 : 81 - 89 .

Kong F C , Zhu Q X , Sakthivel R . Finite-time and fixed-time synchronization analysis of fuzzy Cohen-Grossberg neural networks with discontinuous activations and parameter uncertainties [J ] . European Journal of Control , 2020 , 56 : 179 - 190 .

Zhang X , Zhou W N , Karimi H R , et al . Finite- and fixed-time cluster synchronization of nonlinearly coupled delayed neural networks via pinning control [J ] . IEEE Transactions on Neural Networks and Learning Systems , 2021 , 32 ( 11 ): 5222 - 5231 .

Jiang J H , Jin X Z , Chi J , et al . Distributed adaptive fixed-time synchronization for disturbed complex networks [J ] . Chaos , Solitons & Fractals, 2023 , 173 : 113612 .

Dong Y , Chen J W , Cao J D . Fixed-time pinning synchronization for delayed complex networks under completely intermittent control [J ] . Journal of the Franklin Institute , 2022 , 359 ( 14 ): 7708 - 7732 .

Wang Y B , Min F H , Huang G , et al . Finite-time modified combination synchronization of memristive FitzHugh-Nagumo circuit with unknown disturbances [J ] . Chinese Journal of Physics , 2020 , 67: 590-601(Ch).

Sun J W , Wang Y , Wang Y F , et al . Compound-combination synchronization of five chaotic systems via nonlinear control [J ] . Optik , 2016 , 127 ( 8 ): 4136 - 4143 .

Sun J W , Fang J , Wang Y F , et al . Function combination synchronization of three chaotic complex systems [J ] . Optik , 2016 , 127 ( 20 ): 9504 - 9516 .

Mahmoud G M , Ahmed M E , Abed-Elhameed T M . On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization [J ] . Optik , 2017 , 130 : 398 - 406 .

Xi H L , Li Y X , Huang X . Adaptive function projective combination synchronization of three different fractional-order chaotic systems [J ] . Optik , 2015 , 126 ( 24 ): 5346 - 5349 .

Zheng S . Multi-switching combination synchronization of three different chaotic systems via nonlinear control [J ] . Optik , 2016 , 127 ( 21 ): 10247 - 10258 .

Khan A , Khattar D , Prajapati N . Dual combination combination multi switching synchronization of eight chaotic systems [J ] . Chinese Journal of Physics , 2017 , 55 ( 4 ): 1209 - 1218 (Ch) .

Xiong K L , Yu J , Hu C , et al . Synchronization in finite/fixed time of fully complex-valued dynamical networks via nonseparation approach [J ] . Journal of the Franklin Institute , 2020 , 357 ( 1 ): 473 - 493 .

Chen H K . Synchronization of two different chaotic systems: A new system and each of the dynamical systems Lorenz, Chen and Lü [J ] . Chaos , Solitons & Fractals, 2005 , 25 ( 5 ): 1049 - 1056 .

Kharabian B , Mirinejad H . Synchronization of Rossler chaotic systems via hybrid adaptive backstepping/sliding mode control [J ] . Results in Control and Optimization , 2021 , 4 : 100020 .

Sprott J C . Some simple chaotic flows [J ] . Physical Review E , 1994 , 50 ( 2 ): R647 - R650 .

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