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Solitary routes to chimera states

Leonhard Schülen1, Alexander Gerdes2, Matthias Wolfrum2, and Anna Zakharova1

  • 1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin, Germany
  • 2Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany

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Phys. Rev. E 106, L042203 – Published 24 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.L042203

Abstract

We show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit we demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. We demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators.

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References (30)

  1. Y. Maistrenko, B. Penkovsky, and M. Rosenblum, Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions, Phys. Rev. E 89, 060901(R) (2014).
  2. P. Jaros, S. Brezetsky, R. Levchenko, D. Dudkowski, T. Kapitaniak, and Y. Maistrenko, Solitary states for coupled oscillators with inertia, Chaos 28, 011103 (2018).
  3. L. Schülen, S. Ghosh, A. D. Kachhvah, A. Zakharova, and S. Jalan, Delay engineered solitary states in complex networks, Chaos, Solitons Fractals 128, 290 (2019).
  4. S. Majhi, T. Kapitaniak, and D. Ghosh, Solitary states in multiplex networks owing to competing interactions, Chaos 29, 013108 (2019).
  5. M. Mikhaylenko, L. Ramlow, S. Jalan, and A. Zakharova, Weak multiplexing in neural networks: Switching between chimera and solitary states, Chaos 29, 023122 (2019).
  6. R. Berner, A. Polanska, E. Schöll, and S. Yanchuk, Solitary states in adaptive nonlocal oscillator networks, Eur. Phys. J.: Spec. Top. 229, 2183 (2020).
  7. N. Kruk, Y. Maistrenko, and H. Koeppl, Solitary states in the mean-field limit, Chaos 30, 111104 (2020).
  8. L. Schülen, D. A. Janzen, E. S. Medeiros, and A. Zakharova, Solitary states in multiplex neural networks: Onset and vulnerability, Chaos, Solitons Fractals 145, 110670 (2021).
  9. E. V. Rybalova, A. Zakharova, and G. I. Strelkova, Interplay between solitary states and chimeras in multiplex neural networks, Chaos, Solitons Fractals 148, 111011 (2021).
  10. M. Wolfrum, The turing bifurcation in network systems: Collective patterns and single differentiated nodes, Physica D 241, 1351 (2012).
  11. E. Rybalova, V. S. Anishchenko, G. I. Strelkova, and A. Zakharova, Solitary states and solitary state chimera in neural networks, Chaos 29, 071106 (2019).
  12. F. Hellmann, P. Schultz, P. Jaros, R. Levchenko, T. Kapitaniak, J. Kurths, and Y. Maistrenko, Network-induced multistability through lossy coupling and exotic solitary states, Nat. Commun. 11, 592 (2020).
  13. I. Franović, S. Eydam, N. Semenova, and A. Zakharova, Unbalanced clustering and solitary states in coupled excitable systems, Chaos 32, 011104 (2022).
  14. A. Zakharova, Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise and Delay (Springer, New York, 2020).
  15. Y. Kuramoto and D. Battogtokh, Coexistence of coherence and incoherence in nonlocally coupled phase oscillators, Nonlin. Phenom. Complex Syst. 5, 380 (2002).
  16. D. M. Abrams and S. H. Strogatz, Chimera States for Coupled Oscillators, Phys. Rev. Lett. 93, 174102 (2004).
  17. S. W. Haugland, A. Tosolini, and K. Krischer, Between synchrony and turbulence: Intricate hierarchies of coexistence patterns, Nat. Commun. 12, 5634 (2021).
  18. L. Schmidt and K. Krischer, Clustering as a Prerequisite for Chimera States in Globally Coupled Systems, Phys. Rev. Lett. 114, 034101 (2015).
  19. I. Franović, O. E. Omel'chenko, and M. Wolfrum, Bumps, chimera states, and turing patterns in systems of coupled active rotators, Phys. Rev. E 104, L052201 (2021).
  20. M. Golubitsky and I. Stewart, The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space (Springer Science & Business Media, Berlin, 2003), Vol. 200.
  21. E. J. Doedel, A. R. Champneys, F. Dercole, T. F. Fairgrieve, Y. A. Kuznetsov, B. Oldeman, R. C. Paffenroth, B. Sandstede, X. J. Wang, and C. H. Zhang, Auto-07p: Continuation and bifurcation software for ordinary differential equations, Concordia Univ., Version 0.9.1, 2012; http://sourceforge.net/projects/auto-07p/files/auto07p/.
  22. N. Nakagawa and Y. Kuramoto, From collective oscillations to collective chaos in a globally coupled oscillator system, Physica D 75, 74 (1994).
  23. F. P. Kemeth, B. Fiedler, S. W. Haugland, and K. Krischer, 2-cluster fixed-point analysis of mean-coupled Stuart–Landau oscillators in the center manifold, J. Phys. Complex. 2, 025005 (2021).
  24. M. Wolfrum and O. E. Omel'chenko, Chimera states are chaotic transients, Phys. Rev. E 84, 015201(R) (2011).
  25. D. A. Wiley, S. H. Strogatz, and M. Girvan, The size of the sync basin, Chaos 16, 015103 (2006).
  26. A. Schlüter, D. Lortz, and F. Busse, On the stability of steady finite amplitude convection, J. Fluid Mech. 23, 129 (1965).
  27. W. Eckhaus, Studies in Non-Linear Stability Theory, Springer Tracts in Natural Philosophy (Springer, Berlin, Heidelberg, 1965).
  28. L. Tuckerman and D. Barkley, Bifurcation analysis of the Eckhaus instability, Phys. D (Amsterdam, Neth.) 46, 57 (1990).
  29. K. Okuda, Variety and generality of clustering in globally coupled oscillators, Physica D 63, 424 (1993).
  30. D. Hansel, G. Mato, and C. Meunier, Clustering and slow switching in globally coupled phase oscillators, Phys. Rev. E 48, 3470 (1993).

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Information

Phys. Rev. E 106, L042203– Published 24 October, 2022
  • Received 1 April 2022
  • Accepted 26 September 2022
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