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Extreme multistability (EM) in coupled pendulum clocks generates infinite stable states. Symmetric coupling creates complex dynamics with varying synchronization and group behaviors, highly dependent on initial conditions.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Complex Systems

Background:

  • Extreme multistability (EM) describes systems with infinite coexisting attractors, leading to complex dynamics.
  • Understanding EM is crucial for predicting the long-term behavior of many physical and engineering systems.

Purpose of the Study:

  • To investigate the induction of extreme multistability in a model of coupled pendulum clocks.
  • To analyze how specific coupling schemes influence the emergence of complex dynamical behaviors.

Main Methods:

  • Analysis of a dynamical system model of four coupled pendulum clocks on an oscillating base.
  • Investigation of symmetric cross-coupling schemes to induce EM.
  • Characterization of coexisting stable states and their synchronization properties.
  • Examination of basins of attraction to understand initial condition dependence.

Main Results:

  • Symmetric coupling successfully induces extreme multistability in the pendulum clock system.
  • Infinitely many coexisting stable states, including periodic and synchronized states, were observed.
  • Observed states exhibited diverse phase synchronization patterns, including in-phase and anti-phase dynamics.
  • System behavior showed a complex dependence on initial conditions, with distinct groups of pendulums exhibiting different behaviors.

Conclusions:

  • Symmetric coupling is an effective method for inducing extreme multistability in coupled pendulum systems.
  • The study demonstrates complex dynamical behaviors and synchronization patterns arising from EM.
  • Findings highlight the critical role of initial conditions in determining system outcomes within EM regimes.