Synchronization limit of weakly forced nonlinear oscillators
Synchronization limit of weakly forced nonlinear oscillators
复制标题
弱受迫非线性振荡器的同步极限
DOI：
10.1088/1751-8113/47/40/402002
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Hisa-Aki Tanaka
中科院分区：
文献类型：
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作者：
清藤 博暉;山本 有作;Hisa-Aki Tanaka
非线性振子对外部周期强迫表现出同步（注入锁定），这是非线性振子网络相互同步的基础。尽管有同步的历史和注入锁定的实际重要性，但对于给定的振荡器，有效的注入锁定仍然存在许多重要的开放问题。在这项工作中，我阐明了在弱强迫下控制同步限制的隐藏机制，这与一个广为人知的不等式有关；持有人ʼ年代不平等。这种机制使我们能够理解高效的注入锁定是如何以及为什么实现的；构造了同步极限的一般理论，系统地阐明了包括脉冲序列在内的一般强迫的同步范围的最大化或同步的稳定性，以及一般m: n锁相的基本极限。以霍奇金-赫胥黎神经元模型为例，系统地验证了这些同步限制及其效用。
Nonlinear oscillators exhibit synchronization (injection-locking) to external periodic forcings, which underlies the mutual synchronization in networks of nonlinear oscillators. Despite its history of synchronization and the practical importance of injection-locking to date, there are many important open problems of an efficient injection-locking for a given oscillator. In this work, I elucidate a hidden mechanism governing the synchronization limit under weak forcings, which is related to a widely known inequality; Hölderʼs inequality. This mechanism enables us to understand how and why the efficient injection-locking is realized; a general theory of synchronization limit is constructed where the maximization of the synchronization range or the stability of synchronization for general forcings including pulse trains, and a fundamental limit of general m: n phase locking, are clarified systematically. These synchronization limits and their utility are systematically verified in the Hodgkin–Huxley neuron model as an example.