# Effects of local fields in a dissipative Curie-Weiss model: Bautin bifurcation and large self-sustained oscillations

## TL;DR

This paper investigates how adding a random magnetic field to a dissipative Curie-Weiss model influences its macroscopic dynamics, revealing a Bautin bifurcation and the emergence of large self-sustained oscillations under certain conditions.

## Contribution

It demonstrates the existence of a Bautin bifurcation and the formation of large-amplitude oscillations due to the combined effects of the random field and dissipation in the model.

## Key findings

- Existence of a Bautin bifurcation point.
- Emergence of large self-sustained oscillations under strong field and low temperature.
- Periodic orbit arises through a global bifurcation.

## Abstract

We modify the spin-flip dynamics of a Curie-Weiss model with dissipative interaction potential (Dai Pra, Fischer and Regoli (2013)) by adding a site-dependent i.i.d. random magnetic field. The purpose is to analyze how the addition of the field affects the time-evolution of the observables in the macroscopic limit. Our main result shows that a Bautin bifurcation point exists and that, whenever the field intensity is sufficiently strong and the temperature sufficiently low, a periodic orbit emerges through a global bifurcation in the phase space, giving origin to a large-amplitude rhythmic behavior.