Extreme multistability in symmetrically coupled clocks

TL;DR

This paper demonstrates how symmetric coupling in a system of four pendulum clocks can induce extreme multistability, leading to infinitely many coexisting attractors with diverse synchronization states and complex basin structures.

Contribution

It introduces a specific coupling scheme that induces extreme multistability in a symmetric pendulum system, revealing complex attractor coexistence and basin dependence.

Findings

Symmetric coupling increases dynamical complexity.

Multiple stable periodic states coexist with different synchronization patterns.

Basins of attraction show complex dependence on initial conditions.

Abstract

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyse a model for pendulum clocks coupled by springs and suspended on an oscillating base, and show how EM can be induced in this system by a specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.