Course: Dynamical Systems II

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Course title Dynamical Systems II
Course code MU/03051
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study 3
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • MÁLEK Michal, doc. RNDr. Ph.D.
Course content
1. Flow - flow, trajectory, equilibria. 2. Invariant sets - alpha nad omega limit set of the folw, closed orbit, Poincaré - Bendixson Theorem. 3. Bifurcation I. - bifurcation, bifurcation diagram. 4. Examples - pitchfork, transcritical, saddle node and Poincaré - Andronov - Hopf bifurcation. 5. Bifurcation II. - qualitative equivalence of the linear systems, hyperbolic systems, bifurcation of linear systems. 6. Bifurcation III. - Hartman - Grobman and Poincaré - Andronov - Hopf theorems. Examples of nonhyperbolic equilibria, supercritical bifurcation. 7. Centram manifold - central manifolds and their applications.

Learning activities and teaching methods
unspecified
Recommended literature
  • D. K. Arrowsmith, C. M. Place. An introduction to Dynamical Systems. Cambridge University Press, 1990.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematical Methods in Economics (2) Economy 3 Summer
Mathematical Institute in Opava Geometry and Global Analysis (1) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematical Analysis (1) Mathematics courses 2 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 4 Summer
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (3) Economy 3 Summer