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Last update: T_KNM (17.05.2004)
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Last update: JANOVSKY/MFF.CUNI.CZ (03.04.2008)
Theory and numerical methods of bifurcation analysis. |
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Last update: T_KNM (16.05.2008)
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 |
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Last update: T_KNM (16.05.2008)
Lectures in a lecture hall. |
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Last update: T_KNM (16.05.2008)
Examination according to the syllabus. |
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Last update: T_KNM (16.05.2008)
Hopf bifurcation: formulation of Hopf bifurcation Theorem, normal form analysis. Analytical techniques (a survay): Center Manifold and normal form reductions, Lyapunov-Schmidt Reduction. Numerical detection of Hopf bifurcation (construction of test functions).
Codim = 2 bifurcations: cusp, Takens-Bogdanov, Hopf-fold, Hopf-Hopf, degenerate Hopf bifurcation point. Dynamical interpretation (normal form analysis), numerical detection.
Periodic solutions: Poincaré map, stability of an periodic orbit (cycle), variational equation about a cycle. Bifurcation of periodic solutions: fold, period doubling, torus bifurcation.
Symmetry of dynamical systems: group of symmetries (examples), equivariance, equivariant dimensional reduction, symmetry-breaking.
Large dynamical systems: Recursive Projection Method, continuation of invariant subspaces. |
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Last update: T_KNM (16.05.2008)
There are no special entry requirements. |