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 |

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

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

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

To master topics listed below.

Lectures

Tutorials

Project work

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.

[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] 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

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.

No additional requirements are imposed on the student.

Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

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 | 3 |

Show history

Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

Show history

Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | P | Czech | Ostrava | Optional | study plan | |||||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | Optional | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | Optional | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | Choice-compulsory type B | study plan | |||||

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 |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2023/2024 Winter |

2021/2022 Winter |

2019/2020 Winter |