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Collective periodicity in mean-field models of cooperative behavior

  • Francesca Collet
  • Paolo Dai PraEmail author
  • Marco Formentin
Article

Abstract

We propose a way to break symmetry in stochastic dynamics by introducing a dissipation term. We show in a specific mean-field model, that if the reversible model undergoes a phase transition of ferromagnetic type, then its dissipative counterpart exhibits periodic orbits in the thermodynamic limit.

Keywords

Interacting diffusions Random potential Homoclinic bifurcation Mean-field interaction Noise-induced periodicity 

Mathematics Subject Classification

60J60 60K35 37G15 37H20 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Francesca Collet
    • 1
  • Paolo Dai Pra
    • 2
    Email author
  • Marco Formentin
    • 3
  1. 1.Dipartimento di MatematicaAlma Mater Studiorum Università di BolognaBolognaItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di PadovaPaduaItaly
  3. 3.UTIA, Czech Academy of SciencesPragueCzech Republic

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