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Secondary Bifurcation in Nonlinear Diffusion Reaction Equations
Author(s) -
Keener J. P.
Publication year - 1976
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1976553187
Subject(s) - reaction–diffusion system , bifurcation , nonlinear system , type (biology) , mathematics , diffusion , mathematical analysis , stability (learning theory) , bifurcation theory , physics , thermodynamics , computer science , ecology , quantum mechanics , machine learning , biology
A set of two coupled nonlinear diffusion reaction equations is studied and the existence of secondary bifurcation is shown. Using the method of two‐timing, it is found that diffusion reaction equations of this type can exhibit an exchange of stability between distinct nontrivial solutions. This exchange can provide either a smooth or discontinuous transition between stable solutions, and the nontrivial solutions can be either steady or temporally periodic. This analysis is applied to the model biochemical reaction of Prigogine and the types of secondary bifurcation which occur in this model are classified.