* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 470-4120/02 | |||||
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Number of ECTS Credits Allocated | 4 ECTS credits | |||||

Type of Course Unit * | Optional | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | ||||||

Semester when the Course Unit is delivered | Winter Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech, English | |||||

Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

LAM05 | doc. RNDr. Marek Lampart, Ph.D. | |||||

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.
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Learning Outcomes of the Course Unit | ||||||

To master topics listed below. | ||||||

Course Contents | ||||||

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. | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

[1] Hirsch MW, Smale S, Devaney RL. Differential Equations, Dynamical systems, and an Introduction to Chaos. Elsevier – Acadenic Press USA; 2012. ISBN 978-0-12-382010-5
[2] Devaney RL. An Introduction to Chatic Dynamical Systems. Westview Press, USA; 2003. ISBN 978-0-8133-4085-2 | ||||||

[1] Lampart M, Horák J, Ivan I. Úvod do dynamických systémů: teorie a praxe v geoinformatice. Ostrava: VŠB-TU Ostrava; 2013. ISBN 978-80-248-3185-5.
[2] Kratochvíl C, Heriban P. Dynamické systémy a chaos. VUT – Brno; 2010. ISBN 978-80-214-4152-1 [3] Hirsch MW, Smale S, Devaney RL. Differential Equations, Dynamical systems, and an Introduction to Chaos. Elsevier – Acadenic Press USA; 2012. ISBN 978-0-12-382010-5 [4] Devaney RL. An Introduction to Chatic Dynamical Systems. Westview Press, USA; 2003. ISBN 978-0-8133-4085-2 | ||||||

Recommended Reading: | ||||||

[1] Hirsch MW, Smale S, Devaney RL. Differential Equations, Dynamical systems, and an Introduction to Chaos. Elsevier – Acadenic Press USA; 2012. ISBN 978-0-12-382010-5
[2] Devaney RL. An Introduction to Chatic Dynamical Systems. Westview Press, USA; 2003. ISBN 978-0-8133-4085-2 [3] Marotto FR. Introduction to Mathematical Modeling Using Discrete Dynamical Systems. Thomson, USA; 2006. ISBN 0-495-01417-6 [4] Sandefur JT. Discrete Dynamical Systems Theory and Applications. Clarendon Press, England; 1990. ISBN 0-19-853384-5 | ||||||

[1] Hirsch MW, Smale S, Devaney RL. Differential Equations, Dynamical systems, and an Introduction to Chaos. Elsevier – Acadenic Press USA; 2012. ISBN 978-0-12-382010-5
[2] Devaney RL. An Introduction to Chatic Dynamical Systems. Westview Press, USA; 2003. ISBN 978-0-8133-4085-2 [3] Marotto FR. Introduction to Mathematical Modeling Using Discrete Dynamical Systems. Thomson, USA; 2006. ISBN 0-495-01417-6 [4] Sandefur JT. Discrete Dynamical Systems Theory and Applications. Clarendon Press, England; 1990. ISBN 0-19-853384-5 | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Tutorials, Project work | ||||||

Assesment methods and criteria | ||||||

Tasks are not Defined |