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arXiv 1602.05358nlin.CD
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多延迟时间共振混沌同步

Chaos synchronization by resonance of multiple delay times

Manuel Jimenez Martin, Otti D'Huys, Laura Lauerbach, Elka Korutcheva, Wolfgang Kinzel

备注：
9 pages, 7 figures
发表信息：
Phys. Rev. E 93, 022206 (2016)
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摘要：

混沌同步可能出现在具有延迟耦合的非线性单元网络中。研究了两个具有特定比例的大时滞系统的共振所产生的完全同步和亚晶格同步。对于单延迟网络，同步子格的数目由网络环路长度的最大公因子（GCD）决定。我们证明了解析的GCD条件在网络的迭代Bernouilli映射与多个延迟时间和补充我们的分析结果的数值相图，提供参数区域显示完全和子格同步的共振帐篷和Bernouilli映射。我们比较网络与相同的GCD与单一和多个延迟，我们调查的敏感性的相关性之间的失谐耦合的斯图尔特-朗道振荡器的网络中的延迟。此外，GCD条件还允许检测导致非同步网络中的高相关性的时延共振。具体而言，GCD诱导的共振都观察到在一个混沌的非对称网络和延迟耦合噪声线性振荡器的双连接环。

英文摘要：

Chaos synchronization may arise in networks of nonlinear units with delayed couplings. We study complete and sublattice synchronization generated by resonance of two large time delays with a specific ratio. As it is known for single delay networks, the number of synchronized sublattices is determined by the Greatest Common Divisor (GCD) of the network loops lengths. We demonstrate analytically the GCD condition in networks of iterated Bernouilli maps with multiple delay times and complement our analytic results by numerical phase diagrams, providing parameter regions showing complete and sublattice synchronization by resonance for Tent and Bernouilli maps. We compare networks with the same GCD with single and multiple delays, and we investigate the sensitivity of the correlation to a detuning between the delays in a network of coupled Stuart-Landau oscillators. Moreover, the GCD condition also allows to detect time delay resonances leading to high correlations in non-synchronizable networks. Specifically, GCD-induced resonances are observed both in a chaotic asymmetric network and in doubly connected rings of delay-coupled noisy linear oscillators.

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