Extreme multistability in symmetrically coupled clocks

Zhen Su; Jürgen Kurths; Yaru Liu; Serhiy Yanchuk

doi:10.1063/5.0145733

Extreme multistability in symmetrically coupled clocks

Chaos. 2023 Aug 1;33(8):083157. doi: 10.1063/5.0145733.

Authors

Zhen Su^{1

2}, Jürgen Kurths^{1

3}, Yaru Liu^{1

4}, Serhiy Yanchuk^{1

5}

Affiliations

¹ Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany.
² Department of Computer Science, Humboldt-Universität zu Berlin, 12489 Berlin, Germany.
³ Department of Physics, Humboldt-Universität zu Berlin, 12489 Berlin, Germany.
⁴ Department of Mathematics, Jinan University, 510632 Guangzhou, China.
⁵ Institute of Mathematics, Humboldt-Universität zu Berlin, 12489 Berlin, Germany.

PMID: 38060801
DOI: 10.1063/5.0145733

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 analyze 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 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.