Effects of Local Fields in a Dissipative Curie-Weiss Model

Collet, F.; Formentin, Marco

Effects of Local Fields in a Dissipative Curie-Weiss Model

Bautin Bifurcation and Large Self-sustained Oscillations

Journal article (2019)

Authors

F. Collet Università degli Studi di Padova, Applied Probability -

Marco Formentin Università degli Studi di Padova, Padova Neuroscience Center

Research Group

Applied Probability () (TU Delft)

Mean-field interaction Bautin bifurcation Collective noise-induced periodicity Disordered systems Non-equilibrium systems Random potential Saddle-node bifurcation of periodic orbits

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http://resolver.tudelft.nl/uuid:94cb2a99-a191-4ee8-97fb-05a12ecd9dad

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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Applied Probability

Abstract

We modify the spin-flip dynamics of a Curie-Weiss model with dissipative interaction potential [7] 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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