Czech

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Institute of Computer Aided Engineering and Computer Science (AIU)

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theoretical mechanics, kinetic theory, basics of set theory, linear algebra, basic numeric methods, programming in OOP language

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Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1. Basic terminology - definition of continuous dynamic system, phase space, status variables, configuration space, solution of dynamic system, trajectories.
2. Fixed points, phase portrait, autonomous systems, using of operator of flow.
3. Planar linear systems analysis, canonical systems, criteria of classification, reduction of configuration space, qualitative equivalence, topological classification of planar systems
4. 3D systems, diffeomorfisms, first return map of Poincare, eigenspaces, hyperbolic and non-easy points.
5. Non-linear systems, local linearization, asymptotic and neutral stability, hyperbolic orbits, tangent spaces, limit set, limit cycle, attractor.
6. Attracting sets and basins of attraction, period doubling, Ljapunov exponents, chaotic behaviour.
7. Conservative and dissipative systems and their differences from viewpoint of evolution.
8. Homoclinic and heteroclinic structures, structural stability and bifucations, bifurcation diagrams.
9. Fractal dimension of strange attractors and boundaries of basins of attraction.
10. Symbolic dynamic, non-linear time series analysis.
11. Basics of numerical methods and algorithms for observing dynamic system behaviuor.
12-13. Simulation of physical dynamic systems, investigation of their non-linear phenomena.

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Introduction to Dynamic Systems Theory, programming skills for simulation of dynamic systems evolution and analysis of their non-linear phenomena

Extent and forms are specified by guarantor’s regulation updated for every academic year.

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39 hours, obligation not entered