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Bifurcations in a Bistable Reaction‐Diffusion System
Author(s) -
Ebeling Werner,
Malchow Horst
Publication year - 1979
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.19794910205
Subject(s) - bistability , reaction–diffusion system , homogeneous , diffusion , bifurcation , catastrophe theory , statistical physics , dynamical systems theory , type (biology) , physics , bifurcation theory , thermodynamics , quantum mechanics , nonlinear system , ecology , geotechnical engineering , biology , engineering
The bifurcations of stationary solutions of bistable reaction‐diffusion systems and especially the model due to Schlögl are investigated. The paper is based on the observation that these dynamical systems belong to the gradient type, i.e. methods of topological investigation of the corresponding potential may be applied. Three different types of models are discussed: 1. Homogeneous model; 2. Compartmental model with diffusion; 3. Continuous model with diffusion. Bifurcation maps and relations to catastrophe theory are given.