In this section
@article{Fucho-Rius:2025:10.1103/physreve.111.024213,
author = {Fucho-Rius, M and Maretvadakethope, S and Haro, À and Alarcón, T and Sardanyés, J and Pérez-Carrasco, R},
doi = {10.1103/physreve.111.024213},
journal = {Physical Review E},
title = {Local nearby bifurcations lead to synergies in critical slowing down: the case of mushroom bifurcations},
url = {http://dx.doi.org/10.1103/physreve.111.024213},
volume = {111},
year = {2025}
}
TY - JOUR
AB - 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 (orbifurcations) in a phenomenon known as critical slowing down, and are observed in electronic circuits, circuitquantum 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 timerswith transients much larger than the typical timescales of the reactions involved.
AU - Fucho-Rius,M
AU - Maretvadakethope,S
AU - Haro,À
AU - Alarcón,T
AU - Sardanyés,J
AU - Pérez-Carrasco,R
DO - 10.1103/physreve.111.024213
PY - 2025///
SN - 2470-0045
TI - Local nearby bifurcations lead to synergies in critical slowing down: the case of mushroom bifurcations
T2 - Physical Review E
UR - http://dx.doi.org/10.1103/physreve.111.024213
UR - https://doi.org/10.1103/physreve.111.024213
VL - 111
ER -
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