From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations

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• dc.contributor.author Floriach, Pol
• dc.contributor.author García Ojalvo, Jordi
• dc.contributor.author Clusella, Pau
• dc.date.accessioned 2025-03-18T07:46:36Z
• dc.date.available 2025-03-18T07:46:36Z
• dc.date.issued 2025
• dc.description.abstract Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can, thus, expect complex dynamics to arise in networks of such populations. Here, we analyze the dynamics of networks of populations of heterogeneous mean-field coupled Kuramoto-Sakaguchi oscillators and show that the instability that leads to chimera states in a simple two-population model also leads to extensive chaos in large networks of coupled populations. Formally, the system consists of a complex network of oscillator populations whose mesoscopic behavior evolves according to the Ott-Antonsen equations. By considering identical parameters across populations, the system contains a manifold of homogeneous solutions where all populations behave identically. Stability analysis of these homogeneous states provided by the master stability function formalism shows that non-trivial dynamics might emerge on a wide region of the parameter space for arbitrary network topologies. As examples, we first revisit the two-population case and provide a complete bifurcation diagram. Then, we investigate the emergent dynamics in large ring and Erdös-Rényi networks. In both cases, transverse instabilities lead to extensive space-time chaos, i.e., irregular regimes whose complexity scales linearly with the system size. Our work provides a unified analytical framework to understand the emergent dynamics of networks of oscillator populations, from chimera states to robust high-dimensional chaos.
• dc.description.sponsorship The authors would like to thank Diego Pazó and Alessandro Torcini for useful feedback on this work. P.C. and J.G.O. have received funding from the Future and Emerging Technologies Programme (FET) of the European Union’s Horizon 2020 research and innovation programme (project NEUROTWIN, Grant Agreement No. 101017716). J.G.O. was also financially supported by the Spanish Ministry of Science and Innovation, the Spanish State Research Agency and FEDER (Project Reference No. PID2021-127311NB-I00), and by the ICREA Academia program. This work was done while P.F. was a student at the ETSETB, Universitat Politècnica de Catalunya.
• dc.format.mimetype application/pdf
• dc.identifier.citation Floriach P, Garcia-Ojalvo J, Clusella P. From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations. Chaos. 2025 Feb 1;35(2):023115. DOI: 10.1063/5.0243379
• dc.identifier.doi http://dx.doi.org/10.1063/5.0243379
• dc.identifier.issn 1054-1500
• dc.identifier.uri http://hdl.handle.net/10230/69962
• dc.language.iso eng
• dc.publisher American Institute of Physics
• dc.relation.ispartof Chaos. 2025 Feb 1;35(2):023115
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/101017716
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PE/PID2021-127311NB-I00
• dc.rights © 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/). https://doi.org/10.1063/5.0243379
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by-nc/4.0
• dc.title From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion