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arXiv · 2405.19947

Universal finite-time scaling in the transcritical, saddle-node, and pitchfork discrete and continuous bifurcations

Alvaro Corral
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Abstract

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.

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Alvaro Corral. 2024-05-30. Universal finite-time scaling in the transcritical, saddle-node, and pitchfork discrete and continuous bifurcations. https://arxiv.org/abs/2405.19947

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