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Theory and numerical methods for bifurcation analysis.
Last update: T_KNM (29.04.2015)
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The subject is terminated by an oral examination. Last update: Janovský Vladimír, prof. RNDr., DrSc. (10.06.2019)
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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
Govaerts, W.: Numerical methods for bifurcations of dynamical equilibria, SIAM 2000
Di Bernardo, M. at al: Piecewise-smooth dynamical systems. Theory and applications.
Springer Verlag, New York 2008 Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
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Oral exam according to syllabus. Last update: Janovský Vladimír, prof. RNDr., DrSc. (10.06.2019)
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1) Hopf bifurcation (motivating examples, Hopf bifurcation theorem (approaches to proofs), numerical detection (test functions). 2) Steady state bifurcation of higher codimension (cusp, Takens-Bogdanov, Hopf-fold, Hopf-Hopf, Degenerate Hopf): Dynamical interpretation, normal forms, numerical detection. 3) Periodic solutions (Poincare map, stability of a periodic orbit, variational equation about a cycle). Bifurcation of periodic solutions (fold, period doubling, torus bifurcation). 4) Symmetry of dynamical systems (group of symmetries, symmetry breaking). 5) Non-smooth dynamical systens (examples). Filippov convex method. Classification of piecewise-smooth vector fields. Last update: Kaplický Petr, doc. Mgr., Ph.D. (09.06.2015)
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Bc in mathematics Last update: Janovský Vladimír, prof. RNDr., DrSc. (15.05.2018)
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