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• W2091170017 abstract "The fundamental open problem in bifurcation theory is to determine when linearization and construction are valid. This problem and the problem of matching a critical exponent with a bifurcation point are solved through the application of selection rules. Selection rules are also central for a classification theory which is a natural extension of the above problems. Solutions are classified by four equivalence relations differing in their coarseness. Canonical function bases and bifurcation points are studied. The direction of increased vanishing of integrals involved in existence theorems correspond to various interesting similar order relations, for example to increased phase symmetry and decreased solution symmetry. The symmetries of physical and phase spaces are correlated and the closure of the solutions under the symmetry group is shown and analyzed. The common group theoretical basis for equilibrium and nonequilibrium transitions is emphasized throughout. Thus in both settings the same selection rules determine if the transition is continuous or discontinuous. A theory of symmetry breaking for nonequilibrium-bifurcation systems is described. After discussion of stability and jumps, the theory and the history of potentials in chemical systems far from equilibrium are reviewed from the mathematical, thermodynamic and catastrophe theory points of view. Implications to biological control, morphogenesis and pattern formation are briefly indicated. Throughout, reaction-diffusion is of central importance and it also serves as a carrier for the general ideas in bifurcation theory ." @default.
• W2091170017 created "2016-06-24" @default.
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• W2091170017 date "1980-09-01" @default.
• W2091170017 modified "2023-09-27" @default.
• W2091170017 title "Classification in bifurcation theory and reaction-diffusion systems" @default.
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• W2091170017 doi "https://doi.org/10.1016/0370-1573(80)90008-3" @default.
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