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Course, academic year 2018/2019
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Bifurcation Analysis of Dynamical Systems 2 - NNUM300
Title in English: 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 [hours/week]
Capacity: unlimited
Min. number of students: unlimited
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
Annotation -
Last update: T_KNM (17.05.2004)
Hopf bifurcation. Bifurcation of higher codimensions. Bifurcation of periodic solutions. Symmetry-breaking bifurcation. Large dynamical systems.
Aim of the course -
Last update: JANOVSKY/MFF.CUNI.CZ (03.04.2008)

Theory and numerical methods of bifurcation analysis.

Literature - Czech
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

Teaching methods -
Last update: T_KNM (16.05.2008)

Lectures in a lecture hall.

Requirements to the exam -
Last update: T_KNM (16.05.2008)

Examination according to the syllabus.

Syllabus -
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.

Entry requirements -
Last update: T_KNM (16.05.2008)

There are no special entry requirements.

 
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