# 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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References in periodicals archive ?
Now we explain the mechanism of the periodic bursting based on nonsmooth bifurcation theory.
Finally, part 4 addresses singularity theory in more detail, discussing bifurcation theory and the close-to-integrable case.
Bifurcation theory has been widely used to investigate dynamic behaviours of nonlinear components, and to make analytical answers on formation of synchronous resonance, dynamical behaviour of induction machines, chaotic oscillations and Ferro resonance oscillations phenomenon in electrical engineering.
NONLINEAR SOLID MECHANICS: BIFURCATION THEORY AND MATERIAL INSTABILITY.
Pardavi-Horvath, "Mathematical modeling of nonlinear waves and oscillations in gyromagnetic structures by bifurcation theory methods," Journal of Electromagnetic Waves and Applications, Vol.
Hale, Methods of Bifurcation Theory, Springer, New York, 1982.
In classical bifurcation theory , a standard assumption made is that there is a trivial solution from which bifurcation is to occur.
The research interests of George Isac also embrace a wide range of topics, with main contributions in Nonlinear Analysis, Convexity, Optimization, Complementarity Theory, Bifurcation Theory, Optimal Control, Dynamical systems, Numerical Methods, Nonlinear Analyses in Cones, Stochastic Processes and other.
By using the bifurcation theory of discrete system in , 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).

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