Steindl, A. (2018). Static and Dynamic Bifurcations. In H. Altenbach & A. Öchsner (Eds.), Encyclopedia of Continuum Mechanics (pp. 1–9). Springer-Verlag. https://doi.org/10.1007/978-3-662-53605-6_6-1
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Book Title:
Encyclopedia of Continuum Mechanics
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Related Publication(s):
Encyclopedia of Continuum Mechanics
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Abstract:
Steady solutions of differential equations may lose their stability under parameter variations, and new solution types, e.g., periodic solutions, may emerge. To explore the dynamics close to the loss of stability, the originally high-dimensional system is reduced to a low-dimensional set of bifurcation equations by center manifold theory. The reduced system can be simplified further by normal form theory. These methods are demonstrated for the Hopf bifurcation, when a pair of complex eigenvalues crosses the imaginary axis and a family of periodic solutions branches off from the static equilibrium.
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Keywords:
Stability; Center manifold; Hopf bifurcation; Normal form; Singularity
