470-4120/01 – Dynamical Systems (DS)
| Gurantor department | Department of Applied Mathematics | Credits | 4 |
| Subject guarantor | prof. RNDr. Marek Lampart, Ph.D. | Subject version guarantor | prof. RNDr. Marek Lampart, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Optional |
| Year | | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2015/2016 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
To master topics listed below.
Teaching methods
Lectures
Tutorials
Project work
Summary
The subject is determined to students from the first and also second year of master studies at FEI VŠB-TUO Ostrava and it belongs to the basic mathematical subjects of the technical studies at universities. The subject contains introduction to discrete and continuous dynamic systems. There are introduced classical population, economical and infection models together with standard tools for their dynamic analysis.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Tests during the semester:
Test on the topic of discrete dynamic systems - max. 10 points.
Test on the topic of continuous dynamic systems - max. 10 points.
Individual project on the topic of discrete dynamic system - max. 10 points.
Individual project on the topic of continuous dynamic systems - max. 10 points.
Conditions for the credit:
To accomplish two tests - max. 20 points
To solve two individual projects - max. 20 points.
The maximal number of points from the practical part is 40.
The minimal value of points is demanded 20 for the credit.
E-learning
Other requirements
No additional requirements are imposed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Talks:
One-dimensional and two-dimensional population, economical and infection discrete models. General definition of dynamic system and its stability. The system of quadratic functions and its bifurcation diagram. Symbolic dynamics, topological conjugacy, transitivity and sensitivity on initial conditions. Introduction of chaos. Lyapunov exponents.
Difference equations of the first order (continuous logistic model, Poincaré map). Planar continuous linear systems. Phase portraits of the planar systems (classification of dynamic properties). Nonlinear continuous systems (continuous dependence on initial conditions). Equilibria of nonlinear systems (saddles, stability, bifurcation). Closed orbits and limit sets (Poncaré-Bewndrixon Theorem)
Practice:
Solving problems on the topic: modeling of discrete dynamic systems.
Solving problems on the topic: analysis of properties of discrete dynamic systems.
Solving problems on the topic: classification of chaotic behavior of discrete dynamic systems.
Solving problems on the topic: modeling of continuous dynamic systems.
Solving problems on the topic: analysis of properties of continuous dynamic systems
Solving problems on the topic: classification of chaotic behavior of continuous dynamic systems.
Individual projects:
Two individual projects on the topic:
Discrete dynamic systems.
Continuous dynamic systems.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks