网络化离散时间系统中的耦合诱导周期窗口
Coupling-induced periodic windows in networked discrete-time systems
摘要：
网络化非线性系统由于其单元之间的相互作用而呈现出各种涌现现象。这些系统的一个有趣的特点是存在稳定的周期性行为，即使每个单元振荡混沌，如果在隔离。令人惊讶的是，网络相互作用通过周期性取代混沌的机制仍然知之甚少。在这里，我们表明，这种发病的规律性可以通过复制周期性窗口。这种现象增加了系统参数空间中的稳定域，不仅抑制了混沌，而且使网络不易受到冲击和噪声等外部干扰的影响。此外，我们观察到，网络集群的副本周期窗口对应的参数。为了证实这些意见，我们采用的形式主义的主稳定性函数证明，完全同步状态确实是横向不稳定的副本窗口。
英文摘要：
Networked nonlinear systems present a variety of emergent phenomena as a result of the mutual interactions between their units. An interesting feature of these systems is the presence of stable periodic behavior even when each unit oscillates chaotically if in isolation. Surprisingly, the mechanism in which the network interaction replaces chaos by periodicity is still poorly understood. Here, we show that such an onset of regularity can occur via replication of periodic windows. This phenomenon multiplies the stability domains in the system parameter space, not only suppressing chaos but also making the network less vulnerable to external disturbances such as shocks and noise. Moreover, we observe that the network cluster synchronizes for the parameters corresponding to the replica periodic windows. To confirm these observations, we employ the formalism of the master stability function demonstrating that the complete synchronized state is indeed transversally unstable in the replica windows.
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