# bifurcation theory

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## bifurcation theory

[‚bī·fər′kā·shən ‚thē·ə·rē]
(mathematics)
The study of the local behavior of solutions of a nonlinear equation in the neighborhood of a known solution of the equation; in particular, the study of solutions which appear as a parameter in the equation is varied and which at first approximate the known solution, thus seeming to branch off from it. Also known as branching theory.
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Finally, part 4 addresses singularity theory in more detail, discussing bifurcation theory and the close-to-integrable case.
Hale, Methods of Bifurcation Theory, Springer, New York, 1982.
In classical bifurcation theory [9], a standard assumption made is that there is a trivial solution from which bifurcation is to occur.
By using the bifurcation theory of discrete system in [3], we obtain that the Hopf bifurcation can be preserved under discretization by Euler method.
basic bifurcation theory, linear transform theory (Fourier and Laplace transforms), linear systems theory, complex variable techniques .
Topics include complex variables and potential theory (featuring integral representations in a range of analyses methods and nonlinear potential theory in metric spaces), differential equations and nonlinear analysis (mean curvature flow, bifurcation theory, a nonlinear eigenvalue problem, nonlinear elliptic equations with critical and supercritical Sobolev exponents, eigenvalue analysis of elliptical operators and the theory of nonlinear semigroups), and harmonic analysis (integral geometry and spectral analysis, Fourier analysis and geometric combinatories, eigenfunctions of the Laplacian, fractal analysis via function spaces and five reviews of harmonic analysis techniques).
Professor Rosser set out to create a single-volume encyclopedia covering the broad sweep of economic applications for bifurcation theory (the field encompassing the non-linear math specialties of catastrophe and chaos), and to a great extent he has succeeded.
In so doing, they address such topics as the bifurcation theory of systems with time delay, analysis of chaotic dynamics, and the modeling of quantum transport.
He describes groups, group actions and representations, smooth G-manifolds, equivalent bifurcation theory in terms of steady state bifurcation and of dynamics, equivalence and transversality, applications of G-transversality to bifurcation, equivalent dynamics, and dynamical systems on G-manifolds.
She also ties the stories to chaos theory, bifurcation theory, and noise, and connects them to works by Stuart Moulthrop and Natalie Bookchin.
Jean-Michel Grandmont explores the relation between bifurcation theory applied to steady states of a deterministic overlapping generations model and the possibility of sunspot equilibria.
Quasi-periodic bifurcation theory in other settings,

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