# 700.371 (17S) Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing

## Sommersemester 2017

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Erster Termin der LV
06.03.2017 16:00 - 18:00 , L4.1.02 ICT-Lab
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## Überblick

Lehrende/r
LV-Titel englisch
Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing
LV-Art
Vorlesung-Kurs (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechnungspunkte
4.0
Anmeldungen
12 (30 max.)
Organisationseinheit
Unterrichtssprache
Englisch
LV-Beginn
06.03.2017
eLearning

## Zeit und Ort

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## Intendierte Lernergebnisse

This lecture provides some basic knowledges concerning the modeling process of both linear and nonlinear dynamical systems (NDS) in engineering. Both continuous and discrete nonlinear dynamics systems are considered.

Regarding continuous nonlinear dynamical systems, several mathematical models are obtained in forms of ordinary differential equations (ODEs) and/or partial differential equations (PDEs). Each of these equations describes the dynamics of a specific system, scenario, or phenomenon in engineering (Mechanics, Electro-mechanics, Control systems, Electronics, Transportation, Telematics, etc.). For each ODE, the analytical study is considered and several analytical methods are proposed (e.g. Mean/Average method, Harmonic Balance, Multiple time scales, etc.) in order to derive approximate analytical solutions. The stability and bifurcation analysis of ODEs using some well-known classical methods (e.g. Routh-Hurwitz theorem for local stability, and Lyapunov theorem for global stability, Shilnikov theorem for bifurcation and analytic chaos detection) is also considered. Further, several analytical methods for bifurcation analysis and chaos detection in NDS are considered and some specific case studies are considered for illustration. Analytical expressions/formulae are obtained in order to predict the occurrence of a specific bifurcation (e.g. Period-doubling, Sudden-transition, Andronov-hopf bifurcation, pitchfork bifurcation, and Hopf-pitchfork bifurcation).

Regarding discrete dynamical systems, various mathematical models are considered in form of coupled algebraic equations. For each set of coupled equations, the analytical study is considered and several analytical methods are proposed (e.g. iterative or recursive method, and geometrical method) in order to derive analytical solutions. The stability and bifurcation analysis is conducted using some well-known classical methods (e.g. exponential, and graphical methods).

The Lecture also proposes methods and concepts (e.g. Separation of variables, and Fourier analysis) for solving PDEs analytically. The stability analysis of some classical numerical schemes (e.g. Finite difference method, and method of lines) for solving PDEs is considered.

Overall, the main objectives of this lecture are expressed by the following keywords: Mathematical modeling of NDS using ODEs and PDEs, Analytical solutions of ODEs and PDEs, Numerical solutions of ODEs and PDEs, Analog computing of ODEs and PDEs, Stability analysis of ODEs, Stability of the numerical schemes for solving PDEs, Analytical solutions of DNDS (discrete nonlinear dynamical systems), stability analysis of DNDS, Bifurcation analysis and chaos detection in NDS, Cellular Neural Networks (CNNs) and applications in engineering. The general expectation regarding the knowledge to be provided/acquired is as follows:

• Mastering of the basic concepts for modeling nonlinear dynamical systems in engineering. These systems are generally expressed in form of ODEs and/or PDEs.
• Mastering of analytical methods for solving ODEs and PDEs.
• Mastering of analytical methods for solving DNDS (discrete nonlinear dynamical systems) and stability analysis of DNDS.
• Mastering of analytical methods for stability analysis of NDS modeled by ODEs and PDEs.
• Mastering of analytical methods for Bifurcation analysis and Chaos detection in NDS modeled by ODEs and PDEs.
• Development of a theoretical framework for Cellular Neural Networks (CNNs) and applications in Nonlinear dynamics, Transportation (e.g. simulation of traffic flow, Supply chain, Image processing).

## Literatur

[1]- Bernard Zeigler, Tag Kim, and Herbert Praehofer, “Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems,” Academic Press, USA, 2000

[2]- John Guckenheimer and Philip Holmes, “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields,” Applied Mathematical Sciences, 42, Springer-Verlag, New York, 1983

[3]- Michael Taylor, “Partial differential equations: basic theory,” Springer, New York, 1996

[4]- L.O. Chua, T. Roska, “Cellular Neural Networks and Visual Computing: Foundations and Applications,”  Cambridge University Press, 2002.

[5]- L. O. Chua, “Universality and Emergent Computation in Cellular Neural Networks,” Singapore: World Scientific Publishing, 2003

## Prüfungsinformationen

### Beurteilungsschema

Note/Grade Benotungsschema

## Position im Curriculum

• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Information and Communications Engineering: Supplements (NC, ASR) (Wahlfach)
• Wahl aus dem LV-Katalog (Anhang 4) ( 0.0h VK, VO, KU / 14.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Technical Complements (NC, ASR) (Wahlfach)
• Wahl aus dem LV-Katalog (Anhang 5) ( 0.0h VK, VO, KU / 12.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Information and Communications Engineering: Supplements (NC, ASR) (Wahlfach)
• Wahl aus dem LV-Katalog (Anhang 4) ( 0.0h VK, VO, KU / 14.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Technical Complements (NC, ASR) (Wahlfach)
• Wahl aus dem LV-Katalog (Anhang 5) ( 0.0h VK, VO, KU / 12.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Autonomous Systems and Robotics: Advanced (ASR) (Wahlfach)
• Wahl aus dem LV-Katalog (siehe Anhang 3) ( 0.0h VK, VO / 30.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Autonomous Systems and Robotics (WI) (Wahlfach)
• Wahl aus dem LV-Katalog (siehe Anhang 3) ( 0.0h VK, VO / 30.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
• Fach: Free Electives (Freifach)
• Free Electives ( 0.0h XX / 6.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
• Fach: Technischer Schwerpunkt (Intelligent Transportation Systems) (Pflichtfach)
• 1.1-1.3 Vorlesung mit Kurs oder Vorlesung mit Seminar ( 6.0h VK/VS / 12.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
• Fach: Technischer Schwerpunkt (Intelligent Transportation Systems) (Pflichtfach)
• 1.4-1.5 Kurs oder Labor ( 4.0h KU / 6.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
• Fach: Technische Ergänzung II (Pflichtfach)
• 3.4-3.5 Kurs oder Labor ( 4.0h KU / 6.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
• Fach: Informationstechnische Grundlagen (Pflichtfach)
• 3.1'-3.3' Vorlesung und Kurs ( 12.0h VO, KU / 18.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
• Fach: Research Track (Methodischer Schwerpunkt) (Pflichtfach)
• 4.2'-4.3' Theoretisch-Methodische Lehrveranstaltung I/II ( 0.0h VO/VK/VS/KU/PS / 6.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)
• Masterstudium Technische Mathematik (SKZ: 401, Version: 13W.1)
• Fach: Informationstechnik (Wahlfach)
• Nonlinear Dynamics — Modeling, Simulation and Neuro-Computing ( 2.0h VK / 4.0 ECTS)
• 700.371 Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h VC / 4.0 ECTS)

## Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung

Wintersemester 2020/21
• 700.371 VC Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 4.0ECTS)
Wintersemester 2019/20
• 700.371 VC Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 4.0ECTS)
Wintersemester 2018/19
• 700.371 VC Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 4.0ECTS)
Wintersemester 2017/18
• 700.371 VC Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 4.0ECTS)
Sommersemester 2016
• 700.371 VC Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 4.0ECTS)
Sommersemester 2015
• 700.371 VK Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 4.0ECTS)
Sommersemester 2014
• 700.371 KU Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)
Sommersemester 2013
• 700.371 KU Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)