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Bifurcation Analysis of Dynamical Systems 1 - NNUM200

Title:	Bifurkační analýza dynamických systémů 1
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2018
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:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	prof. RNDr. Vladimír Janovský, DrSc.
Classification:	Mathematics > Numerical Analysis
Interchangeability :	NMNV561
Is incompatible with:	NMNV561
Is interchangeable with:	NMNV561

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: JANOVSKY (24.04.2006)

Examples, motivation. Numerical continuation. Dimensional reduction. Classification of singularities. Dynamical systems: steady states.

Aim of the course -

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

Continuation of steady states.

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 (17.05.2008)

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

Manifolds and its numerical continuation: tangent space, solution manifold and its parametrization, continuation, predictor-corrector technique, adaptive step-length.

Dimensional reduction: singular point, corank, bifurcation equation, Lyapunov-Schmidt reduction and its modifications.

Classification of singular points: elements of singularity theory. Detecting singular points: test functions.

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

One-parameter Bifurcation (motivation): Saddle-node (fold), Hopf bifurcation.

Entry requirements -

Last update: T_KNM (16.05.2008)

There are no special entry requirements.