2003/12/30 by Ryoichi Kawai, R. Kawai, X. Sailer +3 · 2 citations
Decision Sciences · Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Probabilistic and Robust Engineering Design #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.69.051104
published as Phys. Rev. E 69, 051104 (2004) · 8 pages, 8 figures
arxiv created 2003/12/30 · openalex publication_date 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 spatially 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 different 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.