Journal of Statistical Physics

, Volume 176, Issue 2, pp 478–491 | Cite as

Effects of Local Fields in a Dissipative Curie-Weiss Model: Bautin Bifurcation and Large Self-sustained Oscillations

  • Francesca ColletEmail author
  • Marco Formentin


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.


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



The authors are grateful to the anonymous referees whose comments and remarks led to a significant improvement of the paper. They also wish to thank Paolo Dai Pra for fruitful and inspiring discussions. FC was supported by The Netherlands Organisation for Scientific Research (NWO) via TOP-1 grant 613.001.552.

Supplementary material


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Authors and Affiliations

  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Dipartimento di Matematica “Tullio Levi-Civita”PadovaItaly
  3. 3.Padova Neuroscience CenterPadovaItaly

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