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Extreme multistability: Attractor manipulation and robustness.

Chittaranjan Hens1, Syamal K Dana1, Ulrike Feudel2

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Extreme multistability, the coexistence of infinite attractors in dynamical systems, is achieved through a novel coupling design. This method enables partial synchronization and reveals robust phenomena even with parameter mismatches.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Extreme multistability involves infinite attractors in dynamical systems.
  • It is linked to partial synchrony and conserved quantities in coupled systems.

Purpose of the Study:

  • To propose a general coupling design for achieving extreme multistability.
  • To explore partial synchronization, including complete and antisynchronization, in coupled systems.

Main Methods:

  • Designing a general coupling strategy for two coupled systems.
  • Investigating the emergence of partial synchronization and conserved quantities.
  • Analyzing the robustness of the phenomenon to parameter mismatches.

Main Results:

  • The proposed coupling design facilitates partial synchronization (complete, antisynchronization, or mixed states).
  • Extreme multistability emerges from these partial synchronization states.
  • The phenomenon is robust against parameter variations in coupled oscillators.

Conclusions:

  • A novel coupling design effectively induces extreme multistability.
  • This approach offers flexibility in controlling attractor amplitudes.
  • The findings highlight the robustness of extreme multistability in coupled dynamical systems.