Local nearby bifurcations lead to synergies in critical slowing down: the case of mushroom bifurcations
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Published version
Author(s)
Type
Journal Article
Abstract
The behavior of nonlinear systems near critical transitions has significant implications for stability, transients,
and resilience in complex systems. Transient times, τ , become extremely long near phase transitions (or
bifurcations) in a phenomenon known as critical slowing down, and are observed in electronic circuits, circuit
quantum electrodynamics, ecosystems, and gene regulatory networks. Critical slowing down typically follows universal laws of the form τ ∼ |μ − μc|
β , with μ being the control parameter and μc its critical value. For instance, β = −1/2 close to saddle-node bifurcations. Despite intensive research on slowing down phenomena for single bifurcations, both local and global, the behavior of transients when several bifurcations are close to each other remains unknown. Here, we investigate transients near two saddle-node bifurcations merging into a transcritical one. Using a nonlinear gene-regulatory model and a normal form exhibiting a mushroom bifurcation diagram we show, both analytically and numerically, a synergistic, i.e., nonadditive, lengthening of transients due to coupled ghost effects and transcritical slowing down. We also show that intrinsic and extrinsic noise play opposite roles in the slowing down of the transition, allowing us to control the timing of the transition without compromising the precision of timing. This establishes molecular strategies to generate genetic timers
with transients much larger than the typical timescales of the reactions involved.
and resilience in complex systems. Transient times, τ , become extremely long near phase transitions (or
bifurcations) in a phenomenon known as critical slowing down, and are observed in electronic circuits, circuit
quantum electrodynamics, ecosystems, and gene regulatory networks. Critical slowing down typically follows universal laws of the form τ ∼ |μ − μc|
β , with μ being the control parameter and μc its critical value. For instance, β = −1/2 close to saddle-node bifurcations. Despite intensive research on slowing down phenomena for single bifurcations, both local and global, the behavior of transients when several bifurcations are close to each other remains unknown. Here, we investigate transients near two saddle-node bifurcations merging into a transcritical one. Using a nonlinear gene-regulatory model and a normal form exhibiting a mushroom bifurcation diagram we show, both analytically and numerically, a synergistic, i.e., nonadditive, lengthening of transients due to coupled ghost effects and transcritical slowing down. We also show that intrinsic and extrinsic noise play opposite roles in the slowing down of the transition, allowing us to control the timing of the transition without compromising the precision of timing. This establishes molecular strategies to generate genetic timers
with transients much larger than the typical timescales of the reactions involved.
Date Issued
2025-02-01
Date Acceptance
2025-01-30
Citation
Physical Review E, 2025, 111 (2)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
111
Issue
2
Copyright Statement
Published by the American Physical Society Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/40103131
Publication Status
Published
Coverage Spatial
United States
Article Number
024213
Date Publish Online
2025-02-28