https://doi.org/10.1140/epjp/s13360-024-04978-7
Regular Article
Various amplitude chimeras in locally coupled limit-cycle oscillators: impact of coupled system size
1
Center for Computational Modelling, Chennai Institut of Technology, 600069, Chennai, Tamilnadu, India
2
Department of Architecture and Engineering Arts, Fine Arts Institute, University of Dschang, P. O. Box 31, Foumban, Cameroon
3
Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I, P. O. Box 812, Yaoundé, Cameroon
4
Center for Nonlinear Systems, Chennai Institut of Technology, 600069, Chennai, Tamilnadu, India
Received:
26
December
2023
Accepted:
2
February
2024
Published online:
24
February
2024
We investigate chimera states in two networks of locally coupled identical paradigmatic limit-cycle oscillators, which are the van der Pol oscillator and the Rayleigh oscillator. The interplay between local dynamics, local coupling, size of the system, and specially prepared initial conditions allows the two ring-networks to generate a lot of amplitude chimera states; a basic amplitude chimera state being a self-organized state made up of spatially separated domains of synchronous oscillations with a large amplitude and asynchronous oscillations with disparate smaller amplitudes and drifting centers of mass. Apart from this classical amplitude chimera state, we report the occurrence of damped amplitude chimera and stable amplitude chimera states that were found previously, and two novel stable amplitude chimera states, namely, traveling amplitude chimera and snaking amplitude chimera states. The traveling amplitude chimera state, that emerges in coupled systems with relatively large size, involves a strongly localized incoherent region that moves slowly and uniformly along the ring-network. As for the snaking amplitude chimera state, that seldom occurs, its incoherent region(s) snakes (snake, respectively) regularly around a fixed position (fixed positions, respectively). Furthermore, while examining the features of the chimera states with respect to the size of the coupled systems, we find that the lifetime of transient amplitude chimera patterns increases with the size of the coupled system. A result that is contrary to previous findings.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
