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arXiv · 1812.07400

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

Francesca Collet·Marco Formentin
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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.

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Francesca Collet, Marco Formentin. 2018-12-17. Effects of local fields in a dissipative Curie-Weiss model: Bautin bifurcation and large self-sustained oscillations. https://doi.org/10.1007/s10955-019-02310-7

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