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Course, academic year 2018/2019
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Bifurcation Analysis of Dynamical Systems 1 - NMNV561
Title in English: Bifurkační analýza dynamických systémů 1
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: prof. RNDr. Vladimír Janovský, DrSc.
Class: M Mgr. NVM
M Mgr. NVM > Volitelné
Classification: Mathematics > Numerical Analysis
Incompatibility : NNUM200
Interchangeability : NNUM200
Annotation -
Last update: T_KNM (29.04.2015)
Methods for numerical continuation.
Literature - Czech
Last update: T_KNM (15.09.2013)

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

Requirements to the exam - Czech
Last update: prof. RNDr. Vladimír Janovský, DrSc. (15.05.2018)

ústní zkouška dle sylabu

Syllabus -
Last update: doc. Mgr. Petr Kaplický, Ph.D. (09.06.2015)

1) Motivation. Examples of dynamical systems.

2) Parameter dependent dynamical systems. Numerical continuation.

3) Dimensional reduction (singular point, corank, bifurcation equation, Lyapunov-Schmidt reduction).

4) Classification of singular points. Detection of singular points (test functions).

5) Steady states of dynamical systems (asymptotic stability, topological equivalence, Hartman-Grobman theorem). Continuation of branches of steady states, loss of stability.

Entry requirements -
Last update: prof. RNDr. Vladimír Janovský, DrSc. (15.05.2018)

Bc in mathematics

 
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