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

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 met...

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Autores principales:	Nechaev, Vasiliy Andreevich, Rybalova, E. V., Strelkova, Galina Ivanovna
Formato:	article
Lenguaje:	EN RU
Publicado:	Saratov State University 2021
Materias:	logistic map ensemble chimera state heterogeneity noise influence Physics QC1-999
Acceso en línea:	https://doaj.org/article/d8f6703a5f5741b5bf7884ddeea66677
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spelling	oai:doaj.org-article:d8f6703a5f5741b5bf7884ddeea666772021-11-30T10:49:45ZInfluence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps0869-66322542-190510.18500/0869-6632-2021-29-6-943-952https://doaj.org/article/d8f6703a5f5741b5bf7884ddeea666772021-11-01T00:00:00Zhttps://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2021/11/nechaev_et_al_943-952.pdfhttps://doaj.org/toc/0869-6632https://doaj.org/toc/2542-1905The 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.Nechaev, Vasiliy AndreevichRybalova, E. V.Strelkova, Galina IvanovnaSaratov State Universityarticlelogistic mapensemblechimera stateheterogeneitynoise influencePhysicsQC1-999ENRUИзвестия высших учебных заведений: Прикладная нелинейная динамика, Vol 29, Iss 6, Pp 943-952 (2021)
institution	DOAJ
collection	DOAJ
language	EN RU
topic	logistic map ensemble chimera state heterogeneity noise influence Physics QC1-999
spellingShingle	logistic map ensemble chimera state heterogeneity noise influence Physics QC1-999 Nechaev, Vasiliy Andreevich Rybalova, E. V. Strelkova, Galina Ivanovna Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
description	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.
format	article
author	Nechaev, Vasiliy Andreevich Rybalova, E. V. Strelkova, Galina Ivanovna
author_facet	Nechaev, Vasiliy Andreevich Rybalova, E. V. Strelkova, Galina Ivanovna
author_sort	Nechaev, Vasiliy Andreevich
title	Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
title_short	Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
title_full	Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
title_fullStr	Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
title_full_unstemmed	Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
title_sort	influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps
publisher	Saratov State University
publishDate	2021
url	https://doaj.org/article/d8f6703a5f5741b5bf7884ddeea66677
work_keys_str_mv	AT nechaevvasiliyandreevich influenceofparametersinhomogeneityontheexistenceofchimerastatesinaringofnonlocallycoupledmaps AT rybalovaev influenceofparametersinhomogeneityontheexistenceofchimerastatesinaringofnonlocallycoupledmaps AT strelkovagalinaivanovna influenceofparametersinhomogeneityontheexistenceofchimerastatesinaringofnonlocallycoupledmaps
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Influence of parameters inhomogeneity on the existence of chimera states in a ring of nonlocally coupled maps

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