The synchronization control of two chaotic oscillatory systems is designed based on DNA strand displacement in the present work. Thus, combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement. Firstly, five chemical reaction modules of double, displacement, adjustment, catalysis and degradation are designed. Based on these five modules, a 3-variable chaotic oscillatory system is designed. Secondly, based on the design principle of coupling terms and theory of stability, synchronization modules and coupling terms are added to three chaotic oscillatory systems to design combination synchronization of three 3-variable chaotic oscillatory systems based on DNA strand displacement. Modules and systems are implemented and tested using visual DSD and Matlab, and the simulation results are presented to demonstrate the effectiveness and correctness of the chemical reaction modules and systems. The combination synchronization of three 3-variable chaotic oscillatory systems is proposed based on DNA strand displacement, which may be extended to the reaction networks of DNA strand displacement and to the combination synchronization of multivariable chaotic oscillatory systems based on DNA strand displacement.

中文翻译：

---

基于DNA链位移的三变量混沌振荡系统及其耦合组合同步。

本文基于DNA链的位移设计了两个混沌振荡系统的同步控制。因此，提出了基于DNA链位移的三个3变量混沌振荡系统的组合同步。首先，设计了双重，置换，调节，催化和降解五个化学反应模块。基于这五个模块，设计了一个三变量混沌振荡系统。其次，基于耦合项的设计原理和稳定性理论，将同步模块和耦合项添加到三个混沌振荡系统中，以基于DNA链位移设计三个3变量混沌振荡系统的组合同步。使用可视化DSD和Matlab实施和测试模块和系统，仿真结果表明了化学反应模块和系统的有效性和正确性。提出了三个基于DNA链位移的3变量混沌振荡系统的组合同步，可以扩展到DNA链位移的反应网络和基于DNA链位移的多变量混沌振荡系统的组合同步。