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Numerical Methods in Bifurcation Theory - NNUM180

Title:	Numerické metody v teorii bifurkace
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2014 to 2017
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Note:	enabled for web enrollment

Guarantor:	prof. RNDr. Vladimír Janovský, DrSc.
Class:	DS, vědecko - technické výpočty
Classification:	Mathematics > Numerical Analysis

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: JANOVSKY (27.02.2007)

Dynamical systems: Examples. Steady states, numerical continuation. Limit points. Hopf bifurcation and its numerical detection. Bifurcation of a higher codimension. Periodic solutions and theirs bifurcations. Continuation of periodic solutions.

Aim of the course -

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

Theory and numerical methods of bifurcation analysis.

Literature -

Last update: T_KNM (17.05.2008)

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 (17.05.2008)

Lectures in a lecture hall.

Requirements to the exam -

Last update: T_KNM (17.05.2008)

There are no special entry requirements.

Syllabus -

Last update: T_KNM (17.05.2008)

Motivation. Examples of dynamical systems: ecology, chemistry, mechanics, population dynamics, etc.

Dynamical systems: vector field, phase flow, steady state, linearization, asymptotic stability, topological equivalence, Hartman-Grobman Theorem.

Continuation of steady states: tangent space, parametrization, predictor-corrector techniques, adaptive step lenght. A limit point and its detection.

The Hopf bifurcation theorem (elements of proofs). Numerical detection (test functions).

Bifurcation of a higher codimension: cusp, Takens-Bogdanov, Hopf-fold, Hopf-Hopf, degenerate Hopf. Dynamical interpretation, numerical detection.

Periodic solutions: Poincare map, the equation in variations. Bifurcation of periodic solutions (fold, period doubling, torus bifurcation). Continuation of periodic solutions.

Entry requirements -

Last update: T_KNM (17.05.2008)

There are no special entry requirements.