文章基本信息

标题：Finite-time scaling in local bifurcations
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作者：Álvaro Corral ; Josep Sardanyés ; Lluís Alsedà 等
期刊名称：Scientific Reports
电子版ISSN：2045-2322
出版年度：2018
卷号：8
期号：1
页码：11783
DOI：10.1038/s41598-018-30136-y
语种：English
出版社：Springer Nature
摘要：Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available.