Department of Physics, PUC-Rio, Caixa Postal 38097, 22451-900, Rio de Janeiro, Brazil.
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain.
Phys Rev E. 2017 Jun;95(6-1):062213. doi: 10.1103/PhysRevE.95.062213. Epub 2017 Jun 16.
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength (ɛ), range of the interaction (α), that can vary from first neighbors to global coupling, and a parameter (β) that allows one to scan continuously from nondelayed to one-time delayed dynamics. In the α-ɛ plane we identify periodic orbits, limit cycles, and chaotic trajectories, and describe how these structures change with delay. These features can be explained by studying the bifurcation diagrams of a two-dimensional nondelayed map. This allows us to understand the effects of one-time delays on CSSs, e.g., regularization of chaotic orbits and synchronization of short-range coupled maps, observed when the dynamics is moderately delayed. Finally, we substitute the logistic map with cubic and logarithmic maps, in order to test the robustness of our findings.
我们研究了耦合 logistic 映射系统的完全同步状态（CSSs），作为三个参数的函数：相互作用强度（ɛ）、相互作用范围（α），可以从第一近邻扩展到全局耦合，以及一个参数（β），允许连续扫描从无延迟到单次延迟动力学。在α-ɛ平面上，我们识别了周期轨道、极限环和混沌轨迹，并描述了这些结构如何随延迟而变化。通过研究二维无延迟映射的分岔图，可以解释这些特征。这使我们能够理解单次延迟对 CSSs 的影响，例如，当动力学适度延迟时，观察到混沌轨道的正则化和短程耦合映射的同步。最后，我们用立方和对数映射替代 logistic 映射，以测试我们发现的稳健性。
