International Center for Complex Systems, Universidade Federal do Rio Grande do Norte, Natal, Rio Grande do Norte CEP 59078-970, Brazil.
Chaos. 2010 Mar;20(1):013131. doi: 10.1063/1.3368693.
In 2006 Fischer et al. reported the phenomenon of zero-lag long-range isochronous synchronization via dynamical relaying in systems with delay [Phys. Rev. Lett. 97, 123902 (2006)]. They reported that when one has two coupled systems A and C, with delay between them, then the introduction of a third coupled element B between A and C will allow them to synchronize even in regions of the parameter space where this was not possible without the presence of B. Here we studied this phenomenon in detail in coupled Rössler oscillators and found that this happens in three different ways, that is, we verified that when there is feedback between A and B this kind of synchronization can happen via antiphase or in-phase synchronization depending on the delay value. The third case occurs via anticipating synchronization and is found when B drives A and C without getting feedback from them. We found similar phenomena in coupled Kuramoto oscillators, which present periodic orbits only and this allowed us to perform analytical calculations. Finally, we studied coupled logistic maps and identify the region where zero-lag long-range synchronization is possible as the region characterized by a negative transversal Lyapunov exponent.
2006 年，Fischer 等人在具有延迟的系统中通过动态中继报告了零滞后长程等时同步的现象[Phys. Rev. Lett. 97, 123902 (2006)]。他们报告说，当有两个具有延迟的耦合系统 A 和 C 时，在 A 和 C 之间引入第三个耦合元件 B 将允许它们即使在没有 B 存在的情况下不可能同步的参数空间区域中也能同步。在这里，我们在耦合 Rössler 振荡器中详细研究了这种现象，发现这种情况有三种不同的方式，也就是说，我们验证了当 A 和 B 之间存在反馈时，这种同步可以通过反相或同相同步发生，具体取决于延迟值。第三种情况是通过预期的同步发生的，当 B 驱动 A 和 C 而不从它们那里获得反馈时就会发生这种情况。我们在耦合 Kuramoto 振荡器中发现了类似的现象，它们只存在周期轨道，这使得我们能够进行分析计算。最后，我们研究了耦合 logistic 映射，并确定了零滞后长程同步可能发生的区域，即具有负横向 Lyapunov 指数的区域。
