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.
Skip Nav Destination
Article navigation
August 2023
Research Article|
August 31 2023
Extreme multistability in symmetrically coupled clocks
Special Collection:
Chimera states: from theory and experiments to technology and living systems
Zhen Su
;
Zhen Su
(Visualization)
1
Potsdam Institute for Climate Impact Research
, 14473 Potsdam, Germany
2
Department of Computer Science, Humboldt-Universität zu Berlin
, 12489 Berlin, Germany
Search for other works by this author on:
Jürgen Kurths
;
Jürgen Kurths
(Supervision)
1
Potsdam Institute for Climate Impact Research
, 14473 Potsdam, Germany
3
Department of Physics, Humboldt-Universität zu Berlin
, 12489 Berlin, Germany
Search for other works by this author on:
Yaru Liu
;
Yaru Liu
a)
(Writing – original draft)
1
Potsdam Institute for Climate Impact Research
, 14473 Potsdam, Germany
4
Department of Mathematics, Jinan University
, 510632 Guangzhou, China
a)Author to whom correspondence should be addressed: yaruliu879@jnu.edu.cn
Search for other works by this author on:
Serhiy Yanchuk
Serhiy Yanchuk
(Supervision)
1
Potsdam Institute for Climate Impact Research
, 14473 Potsdam, Germany
5
Institute of Mathematics, Humboldt-Universität zu Berlin
, 12489 Berlin, Germany
Search for other works by this author on:
a)Author to whom correspondence should be addressed: yaruliu879@jnu.edu.cn
Chaos 33, 083157 (2023)
Article history
Received:
February 07 2023
Accepted:
June 30 2023
Citation
Zhen Su, Jürgen Kurths, Yaru Liu, Serhiy Yanchuk; Extreme multistability in symmetrically coupled clocks. Chaos 1 August 2023; 33 (8): 083157. https://doi.org/10.1063/5.0145733
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
Nonlinear model reduction from equations and data
Cecilia Pagliantini, Shobhit Jain
Sex, ducks, and rock “n” roll: Mathematical model of sexual response
K. B. Blyuss, Y. N. Kyrychko
Recent achievements in nonlinear dynamics, synchronization, and networks
Dibakar Ghosh, Norbert Marwan, et al.
Related Content
Multistability and basin stability in coupled pendulum clocks
Chaos (October 2019)
Extreme multistability: Attractor manipulation and robustness
Chaos (May 2015)
Time dependent stability margin in multistable systems
Chaos (September 2018)
Long-period clocks from short-period oscillators
Chaos (August 2017)