吸引耦合网络中排斥链接对挫折的影响
Effect of repulsive links on frustration in attractively coupled networks
摘要：
研究了极限环振子网络中吸引-排斥相互作用的影响。主要研究了复杂网络中相邻节点之间产生反相态的设计原理。我们建立了一个部分负控制的正耦合的极限环振荡器内的生成树的分支有效地工作，以及与随机选择的负链接建立零挫折（反相同步）在二分图。基于零挫折的出现，我们开发了一个通用的0- $π$规则来理解二部图中的反相同步。此外，这一规则被用来构造一个非二部图给定的非零挫折值。最后，通过对任意吸引排斥耦合极限环振子的无向非二部图的求解，证明了0- $π$规则的通用性，并成功地计算出了与数值结果相吻合的非零阻挫值.通过小网络的分岔分析验证了该规则的有效性。我们的工作可能揭示存在于具有混合型耦合的振子网络中的几种同步现象的潜在机制。
英文摘要：
We investigate the impact of attractive-repulsive interaction in networks of limit-cycle oscillators. Mainly we focus on the design principle for generating an anti-phase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit-cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (anti-phase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-$π$ rule to understand the anti-phase synchronization in a bipartite graph. Further, this rule is used to construct a non-bipartite graph for a given non-zero frustrated value. We finally show the generality of 0-$π$ rule by implementing it in arbitrary undirected non-bipartite graphs of attractive-repulsively coupled limit-cycle oscillators and successfully calculate the non-zero frustration value which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks. Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.
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