Extreme multistability in symmetrically coupled clocks

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.