470-4120/01 – Dynamical Systems (DS)

Gurantor departmentDepartment of Applied MathematicsCredits4
Subject guarantordoc. RNDr. Marek Lampart, Ph.D.Subject version guarantordoc. RNDr. Marek Lampart, Ph.D.
Study levelundergraduate or graduateRequirementOptional
YearSemesterwinter
Study languageCzech
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
LAM05 doc. RNDr. Marek Lampart, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+10

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:

[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

Recommended literature:

[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

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

Další požadavky na studenta

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

Full-time form (validity from: 2015/2016 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30 (30) 10
                Test 1. Written test 10  0
                Test 2. Written test 10  0
                Projekt Project 10  0
        Examination Examination 70  21
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava Optional study plan
2019/2020 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava Choice-compulsory type B study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava Choice-compulsory type B study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner