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Stochastic Bifurcations in a Bistable Reaction‐Diffusion System with Neumann Boundary Conditions
Author(s) -
Malchow H.,
Ebeling W.,
Feistel R.,
SchimanskyGeier L.
Publication year - 1983
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19834950206
Subject(s) - bistability , fokker–planck equation , neumann boundary condition , bifurcation , stationary distribution , statistical physics , reaction–diffusion system , probability density function , von neumann architecture , mathematical analysis , boundary (topology) , diffusion , first hitting time model , physics , mathematics , nonlinear system , quantum mechanics , partial differential equation , pure mathematics , statistics , markov chain
It is shown for a special bistable reaction‐diffusion model that an external noise shifts deterministic bifurcation maps or generates new bifurcations. Numerical results and an analytical approximation for the bifurcation map of the stationary probability density distribution of the mean concentration in a discrete model are given. The functional Fokker‐Planck equation is solved approximately.