Crisis in time-dependent dynamical systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917959130152960 |
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| author | Olmi, Simona Politi, Antonio |
| author_facet | Olmi, Simona Politi, Antonio |
| contents | 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 $\exp[-α(\ln δ)^2]$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13152 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crisis in time-dependent dynamical systems Olmi, Simona Politi, Antonio Adaptation and Self-Organizing Systems Disordered Systems and Neural Networks Dynamical Systems Chaotic Dynamics 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 $\exp[-α(\ln δ)^2]$, 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. |
| title | Crisis in time-dependent dynamical systems |
| topic | Adaptation and Self-Organizing Systems Disordered Systems and Neural Networks Dynamical Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2503.13152 |