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Collective Almost Synchronisation in Complex Networks

机译:集体几乎同步复杂网络中的

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摘要

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.
机译:这项工作介绍了集体几乎同步(CAS)现象,该现象描述了一种模式的通用方式,该模式如何以较小的耦合强度出现在复杂的网络中。 CAS现象是由于存在一个近似恒定的局部平均场而出现的,其特征是节点的轨迹围绕周期稳定轨道发展。由于每个节点的行为与其他节点的行为不相关,因此基于统计知识的通用概念将导致人们解释局部常数平均场的出现。与这个普遍的概念相反,我们表明,由于几乎恒定的局部均值场的出现,出现了各种众所周知的较弱形式的同步(几乎是时滞,相位同步和广义同步)。如果通过最小化神经元之间的耦合强度并最大化可能的模式数量在大脑中形成记忆,那么CAS现象就是对此的合理解释。

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