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  Compulsoryoptional 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


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 

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 (1IVT)  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 