Sendiña-Nadal Irene, Letellier Christophe
Complex Systems Group & GISC, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
CORIA-UMR 6614, Normandie Université, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
Chaos. 2017 Oct;27(10):103118. doi: 10.1063/1.5005840.
Synchronization is a very generic process commonly observed in a large variety of dynamical systems which, however, has been rarely addressed in systems with low dissipation. Using the Rössler, the Lorenz 84, and the Sprott A systems as paradigmatic examples of strongly, weakly, and non-dissipative chaotic systems, respectively, we show that a parameter or frequency mismatch between two coupled such systems does not affect the synchronizability and the underlying structure of the joint attractor in the same way. By computing the Shannon entropy associated with the corresponding recurrence plots, we were able to characterize how two coupled nonidentical chaotic oscillators organize their dynamics in different dissipation regimes. While for strongly dissipative systems, the resulting dynamics exhibits a Shannon entropy value compatible with the one having an average parameter mismatch, for weak dissipation synchronization dynamics corresponds to a more complex behavior with higher values of the Shannon entropy. In comparison, conservative dynamics leads to a less rich picture, providing either similar chaotic dynamics or oversimplified periodic ones.
同步是一个非常普遍的过程，在各种各样的动力系统中都很常见，然而，在低耗散系统中却很少被提及。分别使用罗塞尔系统、洛伦兹84系统和斯普罗特A系统作为强耗散、弱耗散和非耗散混沌系统的典型例子，我们表明，两个耦合的此类系统之间的参数或频率失配不会以相同的方式影响同步性和联合吸引子的底层结构。通过计算与相应递归图相关的香农熵，我们能够表征两个耦合的非相同混沌振荡器在不同耗散 regime 中如何组织它们的动力学。对于强耗散系统，所产生的动力学表现出与具有平均参数失配的系统兼容的香农熵值，而对于弱耗散，同步动力学对应于具有更高香农熵值的更复杂行为。相比之下，保守动力学导致的情况不太丰富，要么提供类似的混沌动力学，要么提供过于简化的周期动力学。
