| Course title | Qualitative methods of analysis of non-linear systems |
|---|---|
| Course code | UMB/570 |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Frequency of the course | In each academic year, in the summer semester. |
| Semester | Summer |
| Number of ECTS credits | 5 |
| Language of instruction | Czech |
| Status of course | Compulsory, Compulsory-optional, Optional |
| Form of instruction | unspecified |
| Work placements | unspecified |
| Recommended optional programme components | None |
| Lecturer(s) |
|---|
|
| Course content |
|
Content of lectures: Local methods for equilibrial points to differential equations, Hartman-Grobman theorem, stable, unstable and central variet, Central variet theorem , Normal forms, Poincaré mapping, transversality, structural stability; Local bifurcation, Hopf bifurcation, Fractals, construction of attractors, Takens theorem, Mandelbrot and Julian sets, Sharkhov theorem, Smale horseshoe, symbolic dynamics, homoclinic orbits, Ljapunov exponents, strange attractors. Content of practicals: Solution of concrete models from biology with help of the computer software Mathematica, Matlab, GRIND, Locbif, Fractint.
|
| Learning activities and teaching methods |
Monologic (reading, lecture, briefing), Work with multi-media resources (texts, internet, IT technologies)
|
| Learning outcomes |
|
Qualitative analysis of solutions to systems of ODEs , in particular classification of bifurcation points and the sensitivity to parameters.
Students learn methods of qualitative and sensitivity analysis of differential and difference equations, they learn how to find basic types of bifurcation points analytically an numerically with help of computer programs (Auto and xppaut). |
| Prerequisites |
|
We assume knowledge of ordinary differential equations in the range of UMB/587
UMB/CV587 ----- or ----- UMB/587 |
| Assessment methods and criteria |
|
Oral examination, Interim evaluation
Active attendance of practicals (excused absence permitted). Students should find basic types of bifurcation points either numerically or numerically for a given task (a system od ODE of a boundary value problem) and at oral exam they should show how they understand to the theoretical background. |
| Recommended literature |
|
| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Mathematics for future teachers (1) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Summer |
| Faculty: Faculty of Science | Study plan (Version): Applied Mathematics (2010) | Category: Mathematics courses | 3 | Recommended year of study:3, Recommended semester: Summer |