Universality and hysteresis in slow sweeping of bifurcations

Roie Ezraty, Ido Levin, Omri Gat

Research output: Contribution to journalArticlepeer-review

Abstract

Bifurcations in dynamical systems are often studied experimentally and numerically using a slow parameter sweep. Focusing on the cases of period-doubling and pitchfork bifurcations in maps, we show that the adiabatic approximation always breaks down sufficiently close to the bifurcation, so the upsweep and downsweep dynamics diverge from one another, disobeying standard bifurcation theory. Nevertheless, we demonstrate universal upsweep and downsweep trajectories for sufficiently slow sweep rates, revealing that the slow trajectories depend essentially on a structural asymmetry parameter, whose effect is negligible for the stationary dynamics. We obtain explicit asymptotic expressions for the universal trajectories and use them to calculate the area of the hysteresis loop enclosed between the upsweep and downsweep trajectories as a function of the asymmetry parameter and the sweep rate.

Original languageAmerican English
Article number044206
JournalPhysical Review E
Volume109
Issue number4
DOIs
StatePublished - Apr 2024

Bibliographical note

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© 2024 American Physical Society.

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