Synchronization and Complex Dynamics of Oscillators with Delayed Pulse Coupling
Synchronization and Complex Dynamics of Oscillators with Delayed Pulse Coupling
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DOI：
10.1002/anie.201205214
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发表时间：
2012-01-01
影响因子：
16.6
通讯作者：
Torcini, Alessandro
中科院分区：
文献类型：
--
作者：
Baer, Markus;Schoell, Eckehard;Torcini, Alessandro
耦合非线性振荡器网络通常表现出同步和复杂的动态模式，范围从振荡器簇和部分同步状态到波动模式和时空混沌。新出现的行为很大程度上取决于耦合的类型和强度、网络拓扑以及网络中振荡器的频率分布。同步现象的相关性已被认识到许多重要的生物功能，Winfree 和 Kuramoto 的开创性研究开辟了数学和理论研究的一个具有挑战性的领域。 [1] Belousov–Zhabotinsky (BZ) 反应或耦合电化学振荡器等化学系统以前曾被用来通过实验研究同步和相关现象，例如振荡簇的形成。在BZ系统中，无催化剂背景中的催化剂颗粒[2a]或嵌入非反应性油相中的微流体水滴[2b]形式的振荡器进行扩散耦合，而电化学系统[2c-e]构成了所涉及振荡器的全局全耦合的实现。这些系统被证明是同步研究的灵活测试台，因为振荡器的数量（10-100000）以及振荡器的几何排列可以很容易地改变。 Horvath 等人最近在这个成功故事中又迈出了一步，[3] 他们研究了一对脉冲耦合振荡器，通过连续进料搅拌釜反应器 (CSTR) 实现延迟，该反应器充满振荡 BZ 混合物，并与 BZ 反应的化学活化剂 (AgNO3) 或抑制剂 (BrÀ) 的受控突然释放耦合。反应器在尖峰振荡状态下运行，只有在另一个 CSTR 中记录到尖峰时，才会通过将化学试剂释放到其中一个 CSTR 中来发生耦合。通过改变释放物质的量 Horvath 等人。可以改变耦合强度，并且通过控制释放时间（=脉冲耦合的时间），他们能够引入任意时间延迟。除了实验之外，详细的化学动力学模型还为观察到的行为提供了令人信服的机械解释。[3]他们的研究不仅与非线性化学动力学高度相关，而且与生物学研究的重要领域高度相关，因为大多数生物振荡器（从心脏起搏器到闪烁的萤火虫）实际上都是脉冲耦合的。这一事实激发了大量的数学研究和对其行为的预测，例如 Mirollo 和 Strogatz 证明任意数量的具有兴奋性全对全脉冲耦合的振荡器是同步的。 [4]最近，许多备受瞩目的生物学实验研究（从合成遗传振荡器 [5a] 到椎骨胚胎发育中的分段时钟）都认识到了耦合时间延迟的重要性。 [5]广泛讨论延迟脉冲耦合振荡器的一个重要领域是神经科学。在这种背景下，实验致力于研究两个耦合神经元，[6a]大脑不同区域的同步活动，[6b]以及大型神经元群体中b或g振荡的出现，这些振荡通常可以通过脑电图检测到。[6c]此类实验的重要性导致了神经科学中关于延迟脉冲耦合振荡器的大量计算研究。对于成对的振荡器，人们发现延迟抑制耦合的存在比兴奋耦合更可靠地导致同步。[7a]其他……
Networks of coupled nonlinear oscillators often exhibit synchronization and complex dynamic patterns that range from oscillator clusters and partially synchronized states to wave patterns and spatiotemporal chaos. The emerging behavior depends crucially on the type and strength of the coupling, the network topology, as well as on the frequency distributions of the oscillators in the network. The relevance of synchronization phenomena has been recognized for many important biological functions, and the pioneering studies of Winfree and Kuramoto has opened up a challenging field of mathematical and theoretical study.[1] Chemical systems such as the Belousov–Zhabotinsky (BZ) reaction or coupled electrochemical oscillators have previously been used to study synchronization and related phenomena, such as the formation of oscillatory clusters, experimentally. In the BZ system, the oscillators in the form of catalyst particles in a catalyst-free background [2a] or microfluidic water droplets embedded in a nonreactive oil phase [2b] are coupled diffusively, whereas electrochemical systems [2c–e] constitute a realization of global all-to-all coupling of the involved oscillators. These systems proved to be flexible test beds for synchronization studies, because the number of oscillators (10–100000) as well as the geometrical arrangement of the oscillators can be easily varied. A further step in this success story was recently provided by Horvath et al.,[3] who investigated a pair of pulse-coupled oscillators, with delay realized by continuously fed stirred tank reactors (CSTRs) filled with an oscillatory BZ mixture and coupled to a controlled sudden release of a chemical activator (AgNO3) or inhibitor (BrÀ) of the BZ reaction. The reactors are operated in a regime of spiking oscillations, and coupling occurs through the release of a chemical agent into one of the CSTRs only if a spike is recorded in the other CSTR. By changing the amount of the released substance Horvath etal. could vary the coupling strength, and by controlling the time of release (= time of the pulse coupling) they were able to introduce an arbitrary time delay. A detailed chemical kinetics model provides, in addition to the experiments, a convincing mechanistic explanation of the observed behavior.[3]Their study is highly relevant not only for nonlinear chemical dynamics but also for important fields of biological research, since most biological oscillators—from cardiac pacemakers to flashing fireflies—are, in fact, pulse coupled. This fact motivated a large number of mathematical studies and predictions of their behavior, such as the proof by Mirollo and Strogatz that an arbitrary number of oscillators with excitatory all-to-all pulse coupling synchronize.[4] The importance of a time delay in the coupling has been recognized recently in a number of high-profile experimental studies in biology ranging from synthetic genetic oscillators [5a] to the segmentation clock in the embryonic development of vertebrae.[5] An important field where pulse-coupled oscillators with delay are widely discussed is neuroscience. In this context, experiments have been devoted to the investigation of two coupled neurons,[6a] of the synchronous activity of different regions of the brain,[6b] as well as of the emergence of b or g oscillations in large neuronal populations, which are often detected by electroencephalography.[6c] The importance of such experiments has resulted in numerous computational studies on delayed pulse-coupled oscillators in neuroscience. For pairs of oscillators, it was discovered that the presence of delayed inhibitory coupling leads to synchronization more reliably than does excitatory coupling.[7a] Other …