ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
권호 표지

Nonlinear Noise-Induced Transitions in Active Rotator Model

  • Published : 1998.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate noise-induced transitions in active rotator model with a fluctuating threshold in the presence of an additive noise. The fluctuation of the threshold depends on the additive noise in a nonlinear fashion. In the white-noise limit of the fluctuation, the Fokker-Planck equation of the system reduces to that of the system with correlated linear fluctuation implying that the nonlinearity may be transformed into the correlation of linear noises. We also investigate the system with a nonlinear colored noise which depends on the additive noise as its square. The system shows a single peak, two peaks, and three peaks in its steady state probability distribution according to the noise intensities and the correlation time whose change leads to peak-creating, peak-splitting, and peak-merging transitions.

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. Phys. Rev. A v.43 Cooperative Dynamics in Visual Processing Sompolinsky, H.;Golomb, D.;Kleinfeld, D.
  5. Phys. Rev. B v.48 Arrays of Resistively Shunted Josephson-Junctions in Magnetic Fiel Kim, S.;Choi, M.Y.
  6. Chemical Oscillations, Waves, and Turbulence Kuramoto, Y.
  7. Phys. Rev. B v.31 Sliding Charge-Density Waves as a Dynamic Critical Phenomena Fisher, D.
  8. Physica D v.36 Collective Dynamics of Coupled Oscillators with Random Pinning Strogatz, S.H.;Marcus, C.M.;Westervelt, R.M.;Mirollo, R.E.
  9. Prog. Theor. Phys. v.75 Phase Transitions in Active Rotator Systems Shinomoto, S.;Kuramoto, Y.
  10. Topics in the Theory of Random Noise Stratonovich, R.L.
  11. Neural Networks v.7 Pattern Recognition with Figure-Ground Separation by Generation of Coherent Oscillations Yamaguchi, Y.;Shimizu, H.
  12. Neural Networks v.9 Dynamic Linking Among Neural Oscillators Leads to Flexible Pattern Recognition with Figure-Ground Separation Hirakuar, Y.;Yamaguchi, Y.;Shimizu, H.;Nagai, S.
  13. Noise-Induced Transitions Horsthemke, W.;Fefever, R.
  14. Phys. Rev. E v.49 Mean Field Model for Spatially Extended Systems in the Presence of Multiplicative Noise Van den Broeck, C.;Parrondo, J.M.R.;Armero, J.;Hernandez-Machado, A.
  15. Phys. Rev. Lett. v.73 Noise-Induced Nonequilibrium Phase Transition Van den Broeck, C.;Parrondo, J.M.R.;Toral, R.
  16. Z. Phys. B - Condense Matter v.50 Noise Competition in a Nonlinear System: I. Two Independent Noises Fedchenia, I.I.;Usova, N.A.
  17. Z. Phys. B - Condense Matter v.52 Noise Competition in a Nonlinear System: I. Two Independent Noises Fedchenia, I.I.;Usova, N.A.
  18. Phys. Rev. E v.54 Noise-Induced Transitions in Coupled Oscillator Systems with a Pinning Force Kim, S.;Park, S.H.;Ryu, C.S.
  19. ETRI J. v.18 Nonequilibrium Phenomena in Globally Coupled Active Rotators with Multiplicative and Additive Noises Kim, S.;Park, S.H.;Ryu, C.S.
  20. Phys. Rev. Lett. v.78 Noise-Enhanced Multistability in Coupled Oscillator Systems Kim, S.;Park, S.H.;Ryu, C.S.
  21. Phys. Rev. Lett. v.78 Comment on Noise-Induced Nonequilibrium Phase Transition Kim, S.;Park, S.H.;Ryu, C.S.
  22. Phys. Lett. A v.224 Reentrant Transitions in Globally Coupled Active Rotators with Multiplicative and Additive Noises Kim, S.;Park, S.H.;Doering, C.R.;Ryu, C.S.
  23. Phys. Lett. A v.229 The Fokker-Planck Equation for Arbitrary Nonlinear Noises Kim, S.;Park, S.H.;Ryu, C.S.
  24. SIAM J. Appl. Math. v.34 Stability and Control of Stochastic Systems with Wide-Band Noise Disturbances Blankenship, G.;Papanicolaou, G.C.
  25. The Fokker-Planck Equation Risken, H.