Crisis in Time-Dependent Dynamical Systems

Simona Olmi; Antonio Politi

doi:10.48550/arXiv.2503.13152

Crisis in Time-Dependent Dynamical Systems

Simona Olmi^* (Corresponding Author)
, Antonio Politi^* (Corresponding Author)

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space due to the crossing of the boundary of the basin of attraction. We find that crises occur also in non-autonomous systems although the underlying mechanism is more complex. We show that in the vicinity of the transition, the escape probability scales as exp[−α(lnδ)2], where δ is the distance from the critical point, while α is a model-dependent parameter. This prediction is tested and verified in a few different systems, including the Kuramoto model with inertia, where the crisis controls the loss of stability of a chimera state.

Original language	English
Article number	147202
Number of pages	5
Journal	Physical Review Letters
Volume	134
Issue number	14
Early online date	9 Apr 2025
DOIs	https://doi.org/10.48550/arXiv.2503.13152 https://doi.org/10.1103/PhysRevLett.134.147202
Publication status	Published - 11 Apr 2025

Bibliographical note

A. P. wishes to acknowledge Celso Grebogi for providing useful information. S. O. thanks Matthias Wolfrum for useful discussions in the initial stage of this project.

Funding

S. O. received financial support from the National Centre for HPC, Big Data and Quantum Computing–HPC (Centro Nazionale 01–CN0000013) CUP B93C22000620006 with particular reference to Spoke 8: In Silico Medicine & Omics Data. S. O. received financial support by the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.4 funded by the European Union – NextGenerationEU with the Decree n. 1031 on 17 June 2022 of the Italian Ministry of University and Research. Specifically, the research project funded by NRRP is the National Centre for HPC, Big Data and Quantum Computing - HPC (Centro Nazionale 01 – CN0000013) CUP B93C22000620006 with particular reference to Spoke 8: In Silico Medicine & Omics Data.

Funders	Funder number
National Centre for HPC, Big Data and Quantum Computing	B93C22000620006

Keywords

chaos
collective dynamics
coupled oscillators
dynamics of networks
chaotic systems
dynamical systems
high dimensional systems
multiple time scale dynamics

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Cite this

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abstract = "Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space due to the crossing of the boundary of the basin of attraction. We find that crises occur also in non-autonomous systems although the underlying mechanism is more complex. We show that in the vicinity of the transition, the escape probability scales as exp[−α(lnδ)2], where δ is the distance from the critical point, while α is a model-dependent parameter. This prediction is tested and verified in a few different systems, including the Kuramoto model with inertia, where the crisis controls the loss of stability of a chimera state.",

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Crisis in Time-Dependent Dynamical Systems

Abstract

Bibliographical note

Funding

Keywords

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