Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps

IF 0.5 Q4 PHYSICS, MULTIDISCIPLINARY

Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika Pub Date : 2021-11-30 DOI:10.18500/0869-6632-2021-29-6-943-952

V. Nechaev, E. Rybalova, G. Strelkova

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引用次数: 1

Abstract

The aim of the research is to study the influence of inhomogeneity in a control parameter of all partial elements in a ring of nonlocally coupled chaotic maps on the possibility of observing chimera states in the system and to compare the changes in regions of chimera realization using different methods of introducing the inhomogeneity. Methods. In this paper, snapshots of the system dynamics are constructed for various values of the parameters, as well as spatial distributions of cross-correlation coefficient values, which enable us to determine the regime observed in the system for these parameters. To improve the accuracy of the obtained results, the numerical studies are carried out for fifty different realizations of initial conditions of the ring elements. Results. It is shown that a fixed inhomogeneous distribution of the control parameters with increasing noise intensity leads to an increase in the range of the coupling strength where chimera states are observed. With this, the boundary lying in the region of strong coupling changes more significantly as compared with the case of weak coupling strength. The opposite effect is provided when the control parameters are permanently affected by noise. In this case increasing the noise intensity leads to a decrease in the interval of existence of chimera states. Additionally, the nature of the random variable distribution (normal or uniform one) does not strongly influence the observed changes in the ring dynamics. The regions of existence of chimera states are constructed in the plane of «coupling strength – noise intensity» parameters. Conclusion. We have studied how the region of existence of chimeras changes when the coupling strength between the ring elements is varied and when different characteristics of the inhomogeneous distribution of the control parameters are used. It has been shown that in order to increase the region of observing chimera states, the control parameters of the elements must be distributed inhomogeneously over the entire ensemble. To reduce this region, a constant noise effect on the control parameters should be used.

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参数不均匀性对非局部耦合映射环中嵌合体态存在性的影响

本研究的目的是研究非局部耦合混沌映射环中所有部分元素的控制参数的不均匀性对观察系统中嵌合体状态的可能性的影响，并比较采用不同的不均匀性引入方法实现嵌合体的区域变化。方法。在本文中，我们构建了不同参数值的系统动力学快照，以及相互关联系数值的空间分布，使我们能够确定这些参数在系统中观察到的状态。为了提高所得结果的准确性，对50种不同的环单元初始条件实现进行了数值研究。结果。结果表明，随着噪声强度的增加，控制参数的固定非均匀分布导致观察到嵌合体状态的耦合强度范围增大。因此，强耦合区域的边界比弱耦合区域的边界变化更明显。当控制参数受到噪声的永久影响时，则会产生相反的效果。在这种情况下，增大噪声强度会导致嵌合态存在的时间间隔减小。此外，随机变量分布(正态分布或均匀分布)的性质对观测到的环动力学变化没有很大影响。在“耦合强度-噪声强度”参数平面上构造了嵌合体态的存在区域。结论。研究了不同环元间耦合强度和不同控制参数非均匀分布特性下嵌合体存在区域的变化。结果表明，为了增加观察嵌合体状态的范围，元件的控制参数必须在整个系综上非均匀分布。为了减小这个区域，应该对控制参数使用恒定的噪声效应。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Izvestiya Vysshikh Uchebnykh Zavedeniy-Prikladnaya Nelineynaya Dinamika PHYSICS, MULTIDISCIPLINARY-

CiteScore

1.20

自引率

25.00%

发文量

期刊介绍： Scientific and technical journal Izvestiya VUZ. Applied Nonlinear Dynamics is an original interdisciplinary publication of wide focus. The journal is included in the List of periodic scientific and technical publications of the Russian Federation, recommended for doctoral thesis publications of State Commission for Academic Degrees and Titles at the Ministry of Education and Science of the Russian Federation, indexed by Scopus, RSCI. The journal is published in Russian (English articles are also acceptable, with the possibility of publishing selected articles in other languages by agreement with the editors), the articles data as well as abstracts, keywords and references are consistently translated into English. First and foremost the journal publishes original research in the following areas: -Nonlinear Waves. Solitons. Autowaves. Self-Organization. -Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos. -Applied Problems of Nonlinear Oscillation and Wave Theory. -Modeling of Global Processes. Nonlinear Dynamics and Humanities. -Innovations in Applied Physics. -Nonlinear Dynamics and Neuroscience. All articles are consistently sent for independent, anonymous peer review by leading experts in the relevant fields, the decision to publish is made by the Editorial Board and is based on the review. In complicated and disputable cases it is possible to review the manuscript twice or three times. The journal publishes review papers, educational papers, related to the history of science and technology articles in the following sections: -Reviews of Actual Problems of Nonlinear Dynamics. -Science for Education. Methodical Papers. -History of Nonlinear Dynamics. Personalia.