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Examples, motivation. Numerical continuation. Dimensional reduction.
Classification of singularities. Dynamical systems: steady states.
Last update: JANOVSKY (24.04.2006)
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Continuation of steady states. Last update: JANOVSKY/MFF.CUNI.CZ (03.04.2008)
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Govaerts, W.: Numerical methods for bifurcations of dynamical equilibria, SIAM 2000 Kuznetsov Y.A.: Elements of applied bifurcation theory, Appl. Math. Sci. 112, Spriger Verlag, New York 1998 Hale J., Kocak H.: Dynamics and bifurcations, Springer Verlag, New York 1991 Last update: T_KNM (16.05.2008)
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Lectures in a lecture hall. Last update: T_KNM (16.05.2008)
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Examination according to the syllabus. Last update: T_KNM (16.05.2008)
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Motivation. Examples of dynamical systems (ecology, chemistry, mechanics, population dynamics, etc.).
Manifolds and its numerical continuation: tangent space, solution manifold and its parametrization, continuation, predictor-corrector technique, adaptive step-length.
Dimensional reduction: singular point, corank, bifurcation equation, Lyapunov-Schmidt reduction and its modifications.
Classification of singular points: elements of singularity theory. Detecting singular points: test functions.
Dynamical systems: vector field, phase flow, steady state, linearization, asymptotic stability, topological equivalence, Hartman-Grobman Theorem.
One-parameter Bifurcation (motivation): Saddle-node (fold), Hopf bifurcation. Last update: T_KNM (17.05.2008)
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There are no special entry requirements. Last update: T_KNM (16.05.2008)
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