1999/08/06 by Alexander I. Olemskoi, A. I. Olemskoi, Dmitrii O. Kharchenko +1
Economics, Econometrics and Finance · Physics and Astronomy · #Amplitude #Complex Systems and Time Series Analysis #Complex conjugate #Multiplicative function #Multiplicative noise #Noise (video) #Phase (matter) #Phase transition #Realization (probability) #Stability (learning theory) #State (computer science) #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1134/1.1131244
12 pages, 7 figures, LaTeX
arxiv created 1999/08/06 · openalex publication_date 2000/03/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/31 · openalex updated_date 2026/08/05
The behavior of the most probable values of the order parameter x and the amplitude p of conjugate force fluctuations is studied for a stochastic system with a noise amplitude depending on x as |x|a. It is shown that the phase half-plane x>0 for the canonical pair x, p is divided into isolated regions of large, intermediate, and small values of x. In the first region, the trajectories converge to values of x, p → ∞ as the time t → ∞, and the probability of their realization is negligibly small. In the intermediate region, the configuration point tends to the attraction center corresponding to a stationary ordered state. In the region , the trajectories converge to the point x=p=0 for 0<a<1/2 and to x=0, p → ∞ for 1/2<a≤1. In the former case, the probability of realization of trajectories is finite, while, in the latter case, it is negligibly small, and an absorbing state can be formed.