Nonequilibrium Phenomena in Globally Coupled Active Rotators with Multiplicative and Additive Noises

  • Published : 1996.10.31

Abstract

We investigate noise-induced phase transitions in globally coupled active rotators with multiplicative and additive noises. In the system there are four phases, stationary one-cluster, stationary two-cluster, moving one-cluster, and moving two-cluster phases. It is shown that multiplicative noise induces a bifurcation from one-cluster phase to two-cluster phase. Pinning force also induces a bifurcation from moving phase to stationary phase suppressing the multiplicative noise effect. Additive noise reduces both effects of multiplicative noise and pinning force urging the system to the stationary one-cluster phase. The frustrated effects of pinning force and additive and multiplicative noises lead to a reentrant transition at intermediate additive noise intensity. Nature of the transition is also discussed.

Keywords

References

  1. Biol. Cybern. v.54 A neural cocktail-party processor von der Malsburg, C.;Schneider, W.
  2. Biol. Cybern. v.60 Coherent oscillations: A mechanism of feature linking in the visual cortex Eckhorn, R.;Bauer, R.;Jordan, W.;Brosch, M.;Kruse, W.;Munk, M.;Reitboeck, R.J.
  3. Nature v.338 Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimuli properties Gray, C.M.;Konig, P.;Engel, A.K.;Singer, W.
  4. Neural Networks v.7 Pattern recognition with figure-ground separation by generation of coherent oscillations Yamaguchi, Y.;Shimizu, H.
  5. Neural Networks v.9 Dynamic linking among neural oscillators leads to flexible pattern recognition with figure-ground separation Hirakura, Y.;Yamaguchi, Y.;Shimizu, H.;Nagai, S.
  6. Phys. Rev. A v.43 Copperative dynamics in visual processing Sompolinsky, H.;Golomb, D.;Kleinfeld, D.
  7. Phys. Rev. B v.48 Arrays of resistively shunted Josephson junctions in magnetic fields Kim, S.;Choi, M.Y.
  8. Chemical Oscillations Waves, and Turbulence Kuramoto, Y.
  9. Phys. Rev. B v.31 Sliding charge-density waves as a dynamic critical phenomena Fisher, D.
  10. Physica D v.36 Collective dynamic of coupled oscillators with random pinning Strogatz, S.H.;Marcus, C.M.;Westervelt, R.M.;Mirollo, R.E.
  11. Topics in the Theory of Random Noise Stratonovich, R.L.
  12. J Stat. Phys. v.49 Statistical macrodynamics of large dynamical systems: Case of a phase transition in oscillator communities Kuramoto, Y.;Nishikawa, I.
  13. J. Phys. A v.20 Scaling behavior as the onset of mutual entrainment in a population of interesting oscillators Daido, H.
  14. J. Phys. A v.21 Collecrive synchronization in lattices of non-linear oscillators with randomness Strogatz, S.H.;Mirollo, R.E.
  15. Prog. Theor. Phys. v.77 Local and global self-entrainments in oscillator lattices Sakaguchi, H.;Shinomoto, S.;Kuramoto, Y.
  16. Phys. Rev. A v.45 Clustering in globally coupled phase oscillators Golomb, D.;Hansel, D.;Shraiman, B.;Sompolinsky, H.
  17. Physica D v.63 Variety and generality of clustering in globally coupled oscillators Okuda, K.
  18. Prog. Theor. Phys. v.75 Phase transitions in active rotator systems Shinomoto, S.;Kuramoto, Y.
  19. Noise-Induced Transitions Horsthemke, W.;Lefever, R.
  20. Phys. Rev. Lett. v.73 Noise-induced nonequilibrium phase transition Van den Broeck, C.;Parrondo, J.M.R.;Toral, R.
  21. Phys. Rev. E v.53 Noise-induced phase transitions in globally coupled active rotators Park, S.H.;Kim, S.
  22. Int. J. Bifurcation and Chaos Nonequilibrium phenomena in globally coupled phase oscillators: noise-induced bifurcations, clustering, and switching Park, S.H.;Kim, S.;Han, S.K.
  23. Phys. Lett. A Reentrant transitions in globally coupled active rotators with multiplicative and additive noises Kim, S.;Park, S.H.;Doering, C.R.;Ryu, C.S.
  24. Modeling complex systems: stochastic processes, stochastic differential equations, and Fokker-Plank equations;1990 Complex Systems Summer School Doering, C.R.;Natel(ed.);Stein(ed.)
  25. Physica D v.50 Effect of noise and perturbations on limit cycle systems Kurrer, C.;Schulten, K.
  26. The Fokker-Planck Equation Risken, H.
  27. SIAM J. Appl. Math. v.51 Asymptotically efficient Runge-Kutta methods for a class of Ito and Stratonovich equations Newton, N.J.