Macroscopic limit cycle via pure noise-induced phase transition

Abstract

Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In addition using this approach we investigate patially-extended systems with two degrees of freedom per site. For this system, the analytic solution of the stationary Fokker-Planck equation is not available and a standard mean field approach cannot be used to find noise induced phase transitions. A new approach based on cumulant dynamics predicts a noise-induced phase transition through a Hopf bifurcation leading to a macroscopic limit cycle motion, which is confirmed by numerical simulation.

8 pages, 8 figures

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• Stationary and dynamical properties of finite $N$-unit Langevin models subjected to multiplicative noises
• $N$-dependent Multiplicative-Noise Contributions in Finite $N$-unit Langevin Models: Augmented Moment Approach
• Spatial Pattern Formation in External Noise: Theory and Simulation
• Quantum pure noise-induced transitions: A truly nonclassical limit cycle sensitive to number parity
• Stochastic dynamics and mean field approach in a system of three interacting species
• Stochastic phenomena of synchronization in ensembles of mean-field coupled limit cycle oscillators with two native frequencies
• Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz