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ECTS Course Overview



Dynamical Systems

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

Course Unit Code470-4120/02
Number of ECTS Credits Allocated4 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech, English
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
LAM05doc. 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.
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