Abstract

We investigate the robustness of chimera states under the influence of a nonlinear coupling in the form of a power law with exponent α. Taking as working example the Leaky Integrate-and-Fire model coupled in a 1D ring geometry, we show that the chimera states prevail for large values of the exponent α and small values of the coupling strength, while full synchronization is observed in the opposite ends. Our numerical results indicate that the coupling range R does not influence the frequency of oscillations in the coherent or in the incoherent domains. To the contrary, the R value affects the form of the chimera state: the size of the incoherent domains increase monotonically with R in expense of the size of the coherent ones. As an added value, our numerical results demonstrate that the frequency of oscillations decreases monotonically with the power exponent α. This feature can be useful in controlling the frequency of a network of oscillators by simply varying the nonlinearity exponent in the coupling, without modifying any of the other network attributes or parameters.

Graphical abstract

中文翻译：

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奇美拉州的泄漏与火力动力学与幂律耦合

摘要

我们研究了幂律为α的幂律形式在非线性耦合影响下嵌合态的鲁棒性。以工作实例为例，在一维环形几何体中耦合的泄漏积分与发射模型表明，嵌合态主要用于指数α的大值和耦合强度的小值，而在相反的两端观察到完全同步。我们的数值结果表明，耦合范围R不会影响相干或非相干域中的振荡频率。相反，R值影响嵌合状态的形式：非相干结构域的大小随R单调增加牺牲了连贯的大小。作为一个附加值，我们的数值结果表明，振荡频率随功率指数α单调降低。通过简单地改变耦合中的非线性指数，而无需修改任何其他网络属性或参数，此功能可用于控制振荡器网络的频率。

图形概要