Macroscopic limit cycle via pure noise-induced phase transition

Details Macroscopic limit cycle via pure noise-induced phase transition Macroscopic limit cycle via pure noise-induced phase transition

2003-12-30

arxiv.org/abs/cond-mat/0312688v1

Phys. Rev. E 69, 051104 (2004)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 8 figures

Scientific paper

10.1103/PhysRevE.69.051104

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.

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