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Course, academic year 2018/2019
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Bifurcation Analysis of Dynamical Systems 2 - NMNV562
Title in English: Bifurkační analýza dynamických systémů 2
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
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: 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 : NNUM300
Interchangeability : NNUM300
Annotation -
Last update: T_KNM (29.04.2015)
Theory and numerical methods for bifurcation analysis.
Course completion requirements -
Last update: prof. RNDr. Vladimír Janovský, DrSc. (10.06.2019)

The subject is terminated by an oral examination.

Literature - Czech
Last update: T_KNM (15.09.2013)

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

Govaerts, W.: Numerical methods for bifurcations of dynamical equilibria, SIAM 2000

Di Bernardo, M. at al: Piecewise-smooth dynamical systems. Theory and applications.

Springer Verlag, New York 2008

Requirements to the exam -
Last update: prof. RNDr. Vladimír Janovský, DrSc. (10.06.2019)

Oral exam according to syllabus.

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

1) Hopf bifurcation (motivating examples, Hopf bifurcation theorem (approaches to proofs), numerical detection (test functions).

2) Steady state bifurcation of higher codimension (cusp, Takens-Bogdanov, Hopf-fold, Hopf-Hopf, Degenerate Hopf): Dynamical interpretation, normal forms, numerical detection.

3) Periodic solutions (Poincare map, stability of a periodic orbit, variational equation about a cycle). Bifurcation of periodic solutions (fold, period doubling, torus bifurcation).

4) Symmetry of dynamical systems (group of symmetries, symmetry breaking).

5) Non-smooth dynamical systens (examples). Filippov convex method. Classification of piecewise-smooth vector fields.

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

Bc in mathematics

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