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The Third Type of Chaos in a System of Adaptively Coupled Phase Oscillators with Higher-Order Interactions

Author

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  • Anastasiia A. Emelianova

    (A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia)

  • Vladimir I. Nekorkin

    (A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
    Faculty of Radiophysics, National Research Lobachevsky State University of Nizhny Novgorod, 23 Gagarin Avenue, 603022 Nizhny Novgorod, Russia)

Abstract

Adaptive network models arise when describing processes in a wide range of fields and are characterized by some specific effects. One of them is mixed dynamics, which is the third type of chaos in addition to the conservative and dissipative types. In this work, we consider a more complex type of connections between network elements—simplex, or higher-order adaptive interactions. Using numerical simulation methods, we analyze various characteristics of mixed dynamics and compare them with the case of pairwise couplings. We found that mixed dynamics in the case of simplex interactions is characterized by a very high similarity of a chaotic attractor to a chaotic repeller, as well as a stronger closeness of the sum of the Lyapunov exponents of the attractor and repeller to zero. This means that in the case of three elements, the conservative properties of the system are more pronounced than in the case of two.

Suggested Citation

  • Anastasiia A. Emelianova & Vladimir I. Nekorkin, 2023. "The Third Type of Chaos in a System of Adaptively Coupled Phase Oscillators with Higher-Order Interactions," Mathematics, MDPI, vol. 11(19), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4024-:d:1245408
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    References listed on IDEAS

    as
    1. Emelianova, A.A. & Nekorkin, V.I., 2023. "The influence of nonisochronism on mixed dynamics in a system of two adaptively coupled rotators," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Shchapin, D.S. & Emelianova, A.A. & Nekorkin, V.I., 2023. "A chaotic oscillation generator based on mixed dynamics of adaptively coupled Kuramoto oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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