Letellier Christophe, Sendiña-Nadal Irene, Leyva I, Barbot Jean-Pierre
Rouen Normandie University-CORIA, Avenue de l'Université, F-76800 Saint-Etienne du Rouvray, France.
Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
Chaos. 2023 Sep 1;33(9). doi: 10.1063/5.0156025.
Synchronization of chaotic systems is usually investigated for structurally equivalent systems typically coupled through linear diffusive functions. Here, we focus on a particular type of coupling borrowed from a nonlinear control theory and based on the optimal placement of a sensor-a device measuring the chosen variable-and an actuator-a device applying the actuating (control) signal to a variable's derivative-in the response system, leading to the so-called flat control law. We aim to investigate the dynamics produced by a response system that is flat coupled to a drive system and to determine the degree of generalized synchronization between them using statistical and topological arguments. The general use of a flat control law for getting generalized synchronization is discussed.
混沌系统的同步通常是针对结构等效的系统进行研究的，这些系统通常通过线性扩散函数进行耦合。在此，我们关注一种从非线性控制理论借鉴而来的特殊耦合方式，它基于在响应系统中对传感器（一种测量所选变量的装置）和执行器（一种将驱动（控制）信号应用于变量导数的装置）的最优布置，从而产生所谓的平坦控制律。我们旨在研究与驱动系统平坦耦合的响应系统所产生的动力学，并使用统计和拓扑论据来确定它们之间的广义同步程度。本文还讨论了使用平坦控制律来实现广义同步的一般情况。
