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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2405.19947 |
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| _version_ | 1866909213325787136 |
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| author | Corral, Alvaro |
| author_facet | Corral, Alvaro |
| contents | Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws describing the transient (finite-time) dynamics in discrete dynamical systems close to a bifurcation point, following an approach that was valid for the transcritical as well as for the saddle-node bifurcations. We reformulate those previous results and extend them to other discrete and continuous bifurcations, remarkably the pitchfork bifurcation. In contrast to the previous work, we obtain a finite-time bifurcation diagram directly from the scaling law, without a necessary knowledge of the stable fixed point. The derived scaling laws provide a very good and universal description of the transient behavior of the systems for long times and close to the bifurcation points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal finite-time scaling in the transcritical, saddle-node, and pitchfork discrete and continuous bifurcations Corral, Alvaro Statistical Mechanics Bifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci. Rep. 8(11783), 2018] showed the existence of scaling laws describing the transient (finite-time) dynamics in discrete dynamical systems close to a bifurcation point, following an approach that was valid for the transcritical as well as for the saddle-node bifurcations. We reformulate those previous results and extend them to other discrete and continuous bifurcations, remarkably the pitchfork bifurcation. In contrast to the previous work, we obtain a finite-time bifurcation diagram directly from the scaling law, without a necessary knowledge of the stable fixed point. The derived scaling laws provide a very good and universal description of the transient behavior of the systems for long times and close to the bifurcation points. |
| title | Universal finite-time scaling in the transcritical, saddle-node, and pitchfork discrete and continuous bifurcations |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.19947 |