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Emergent Behaviors of Thermodynamic Kuramoto Ensemble on a Regular Ring Lattice

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Abstract

The temporal evolution of Kuramoto oscillators influenced by the temperature field often appears in biological oscillator ensembles. In this paper, we propose a generalized Kuramoto type lattice model on a regular ring lattice with the equal spacing assuming that each oscillator has an internal energy (temperature). Our lattice model is derived from the thermodynamical Cucker–Smale model for flocking on the 2D free space under the assumption that the ratio between velocity field and temperature field at each lattice point has a uniform magnitude over lattice points. The proposed model satisfies an entropy principle and exhibits emergent dynamics under some sufficient frameworks formulated in terms of initial data and system parameters. Moreover, the phase-field tends to the Kuramoto phase-field asymptotically.

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Acknowledgements

The work of S.-Y. Ha was supported by National Research Foundation of Korea (NRF-2020R1A2C3A01003881), and the work of T. Ruggeri was supported National Group of Mathematical Physics GNFM-INdAM

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, Republic of Korea

    Seung-Yeal Ha

  2. Korea Institute for Advanced Study, Hoegiro 85, 02455, Seoul, Republic of Korea

    Seung-Yeal Ha

  3. Department of Mathematical Sciences, Seoul National University, Seoul, 08826, Republic of Korea

    Hansol Park & Woojoo Shim

  4. Department of Mathematics and Alma Mater Research Center on Applied Mathematics AM2, University of Bologna, Bologna, Italy

    Tommaso Ruggeri

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  1. Seung-Yeal Ha
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  2. Hansol Park
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  3. Tommaso Ruggeri
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  4. Woojoo Shim
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Correspondence to Woojoo Shim.

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Communicated by Michael Kiessling.

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Ha, SY., Park, H., Ruggeri, T. et al. Emergent Behaviors of Thermodynamic Kuramoto Ensemble on a Regular Ring Lattice. J Stat Phys 181, 917–943 (2020). https://doi.org/10.1007/s10955-020-02611-2

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  • DOI: https://doi.org/10.1007/s10955-020-02611-2

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