Fixed-Time Function Combination Synchronization of the Two Chaotic System Groups with Unknown Parameters

LI Dekui; WEI Xingmin; WU Jianjun

doi:10.1051/wujns/2026315471

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Fixed-Time Function Combination Synchronization of the Two Chaotic System Groups with Unknown Parameters

Mathematics | 更新时间：2026-10-29

- Fixed-Time Function Combination Synchronization of the Two Chaotic System Groups with Unknown Parameters
- Wuhan University Journal of Natural Sciences Vol. 31, Issue 5, Pages: 471-480(2026)
- 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：
- DOI：10.1051/wujns/2026315471
  CLC： TP273
- Received：17 March 2025，
  
  Published：24 October 2026
- 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

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