# 700.371 (19W) Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing

## Wintersemester 2019/20

Anmeldefrist abgelaufen.

Erster Termin der LV
02.10.2019 10:00 - 12:00 , B04.1.02 ICT-Labor
Nächster Termin:
18.12.2019 10:00 - 12:00 , B04.1.02 ICT-Labor

## Überblick

Lehrende/r
LV-Titel englisch
Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing
LV-Art
Vorlesung-Kurs (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechungspunkte
4.0
Anmeldungen
7 (30 max.)
Organisationseinheit
Unterrichtssprache
Englisch
LV-Beginn
02.10.2019
eLearning

## 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 investigated for illustration of the concepts. Analytical expressions/formulae are obtained in order to predict the occurrence of a specific type of bifurcation (e.g. Period-doubling, Sudden-transition, Andronov-hopf bifurcation, pitchfork bifurcation, and Hopf-pitchfork bifurcation).

The lecture presents concepts for the design of electronic circuits for solving stiff ODEs .

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, Design of electronic circuits for solving 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 continuous NDS (i.e. 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.
• Mastering of the design of electronic circuits for solving ODEs.
• Development of a theoretical framework for Cellular Neural Networks (CNNs) and applications in Nonlinear dynamics and Transportation (e.g. Solving ODEs and PDES, Simulation of traffic flow, Supply chain, Image processing).

## Lehrmethodik

• The slides are available for the whole lecture. These slides are uploaded in the MOODLE system. The full content of each slide is systematically explained by the Lecturer. Additional examples which are not included in slides will be proposed by the Lecturer to allow good understanding of the information provided.
• The slides contain exercices with solutions for the good understanding of the content of each chapter. These solutions are systematically explained (during the lecture) by the Lecturer.
• The slides contain exercices without solutions to be solved by students during the lecture (this is part of oral exam). The students are fully assisted by the Lecturer in order to obtain correct/exact solutions to the proposed exercices. This will help to check whether the students have understood the chapters or not.
•  The slides contain exercices without solutions to be solved as Homework by students. This will help to test the self-learning potential of students.

## Inhalt/e

• Chapter 1. Fundamentals of nonlinear dynamical systems: Modelling and simulation principles; System identification; General process of modelling; Understanding keywords in the field of dynamic-systems (e.g. continuous dynamical system, discrete dynamical system, stability, equilibrium point, attractor, bifurcation, basins of attraction, chaos, stochasticity, torus, identification, synchronization, control/optimization, etc.); Derivation of models/equations for dynamic systems; Concrete examples of dynamic-systems in engineering and corresponding models/equations.
• Chapter 2. Analysis methods for nonlinear dynamical systems: Analytical methods (Routh-Hurwitz criterion, Lyapunov theorem for global stability, Lyapunov theorem for chaos detection, Shilnikov theorem for chaos detection, the Cadran- Method, the Mean/average method, the Multiple time scales method, etc.); Design principle of analog computers (i.e. Classical analog computing); Application- examples to illustrate the concepts based on aforementioned methods.
• Chapter 3. Analytical solutions of models/equations describing either discrete or continuous dynamical systems:  Analytical solutions of discrete models and stability analysis; Analytical solutions of continuous models and stability analysis;  Approximate analytical solutions of stiff ODES (e.g. van der Pol equation, Rayleigh equation, etc.) using the Mean/average method and the Multiple time scales method.
• Chapter 4. Design of electronic circuits for solving stiff ODEs (Design of analog computers): Design of electronic circuits to perform some basic mathematical operations (Summation, Integration, Differentiation, Amplification, Multiplication, etc.); Basic principle of the design of  electronic circuits for solving ODEs; Application to the design of analog computers for solving different types of stiff ODEs: Operational amplifiers (Op Amps) components are used as analog devices.
• Chapter 5. Analytical solutions of linear partial differential equations (PDEs): Method of separation of variables; Fourier analysis; Homogeneous PDEs; Inhomogeneous/Nonhomogeneous PDEs;  First order PDEs; Second Order PDEs.
• Chapter 6. Analytical methods for bifurcation analysis, chaos detection and control in complex dynamical systems:  Bifurcation diagrams, Lyapunov exponents, Basins of attraction.
• Chapter 7. Basics of the modern analog simulation based on the CNN (Cellular Neural Network) Technology: General overview; Presentation of the CNN paradigm (Chua, and Yang, 1988);  Generalization of the CNN paradigm;  Various representations of the elementary CNN cell; Electronic circuit of the elementary CNN cell;  The full CNN architecture as a generator of nonlinear dynamics;  Application of CNN in solving ODEs; Image processing based on the CNN Technology.

## Erwartete Vorkenntnisse

1. Basic knowledge in applied mathematics

2. Basic knowledge in discrete mathematics

3. Basic knowledge in computational mathematics

4. Basic Knowledge in System theory

5. Basic knowledge in Electronics

## Literatur

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

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

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

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

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

## Prüfungsinformationen

### Prüfungsmethode/n

1.  Type of assessment of the course: Written exam at the end of the lecture

2. Duration: 3 to 4 hours

### Prüfungsinhalt/e

* All chapters of the lecture

(The final exam takes into account all chapters of the lecture.)

### Beurteilungskriterien/-maßstäbe

The following three possibilities/options are offered as evaluation criteria:

Option 1. * Exam without BONUS (100 /%).

Option 2. * Exam (100 /%) + BONUS 1.

•* BONUS 1. Participation in the course (i.e., answers to questions) (25% of the total exam).

Note:the answer to questions is not mandatory.

Option 3. * Exam (100 /%) + BONUS 2.

•* BONUS 2. homework (25% the total of the exam).

Note:The homework is not compulsory.

## 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 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: 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 Mathematics (SKZ: 401, Version: 18W.1)
• Fach: Information and Communications Engineering (Wahlfach)
• 9.9 Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing ( 2.0h VC / 4.0 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 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 2017
• 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)