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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.01270 |
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Table of Contents:
- A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $ε$. The random fluctuations of the system at the critical point are studied when the dynamics starts near equilibrium, in the limit as $ε$ goes to zero. Under a space-time scaling the system can be approximated by a 2-dimensional process lying on the centre manifold of the Hopf's bifurcation and a slow radial component together with a fast angular component are identified. Then the critical fluctuations are described by a "universal" stochastic differential equation whose coefficients are obtained taking the average with respect to the fast variable.