Abstract

In a globally coupled network of chaotically oscillating identical Rössler systems, chimera-like states have been made to exist by strengthening, appropriate links of a node that fall under nonlocal topology with additional weak signals, sequentially to sufficient number of nodes of the network. We find a power-law dependence of the distance of oscillators with the spatial correlation function which reveals that the obtained chimera-like states belong to phase chimera category. Further, we define a quantity R to denote the ratio of nodes with additional weak nonlocal strength and observe that the threshold value of it (R_Th) to trigger chimera-like states changes as we alter the coupling radius. Precisely, we see that R_Th decreases as we increase the coupling radius. When we widen our scope of study to the small-world networks we find that R_Th decreases for higher probability values. In addition, we have shown that the chimera-like states even exist when we restrict the additional weak nonlocal signals to be one-sided. We determine the nature of different dynamical states by using the values of strength of incoherence, in general, and category of chimera-like states by means of spatial correlation function, in particular.

Graphical abstract

中文翻译：

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在混合拓扑的振荡器网络中产生类似嵌合体的状态

摘要

在一个由混沌振荡的相同Rössler系统组成的全局耦合网络中，通过增强属于非局部拓扑结构的节点的适当链接（具有附加的弱信号），使嵌合状态得以存在，并依次连接到网络的足够数量的节点。我们发现振荡器的距离与空间相关函数的幂律相关性，这表明所获得的类似嵌合体的状态属于相位嵌合体类别。此外，我们定义一个数量R来表示具有附加的较弱的非局部强度的节点的比率，并观察到它的阈值（R _Th）会触发类似嵌合状态的改变，这是因为我们改变了耦合半径。确切地说，我们看到R _Th随着耦合半径的增加而减小。当我们将研究范围扩展到小世界网络时，我们发现R _Th对于较高的概率值会减小。另外，我们已经表明，当我们将附加的弱非局部信号限制为单侧时，甚至存在嵌合体状态。我们通常使用不相干强度的值来确定不同动力学状态的性质，特别是利用空间相关函数来确定类似嵌合体状态的状态。

图形概要