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Bifurcation Analysis of Dynamical Systems 2 - NNUM300

Title:	Bifurkační analýza dynamických systémů 2
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vladimír Janovský, DrSc.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNV562
Is incompatible with:	NMNV562
Is interchangeable with:	NMNV562

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Hopf bifurcation. Bifurcation of higher codimensions. Bifurcation of periodic solutions. Symmetry-breaking bifurcation. Large dynamical systems.

Last update: T_KNM (17.05.2004)

Aim of the course -

Theory and numerical methods of bifurcation analysis.

Last update: JANOVSKY/MFF.CUNI.CZ (03.04.2008)

Literature - Czech

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)

Teaching methods -

Lectures in a lecture hall.

Last update: T_KNM (16.05.2008)

Requirements to the exam -

Examination according to the syllabus.

Last update: T_KNM (16.05.2008)

Syllabus -

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.

Last update: T_KNM (16.05.2008)

Entry requirements -

There are no special entry requirements.

Last update: T_KNM (16.05.2008)