# 700.383 (17W) LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing

## Wintersemester 2017/18

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Erster Termin der LV
05.10.2017 12:00 - 14:00 , L4.1.02 ICT-Lab
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## Überblick

Lehrende/r
LV-Titel englisch
LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing
LV-Art
Kurs (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechungspunkte
3.0
Anmeldungen
9 (20 max.)
Organisationseinheit
Unterrichtssprache
Englisch
LV-Beginn
05.10.2017
eLearning

## Intendierte Lernergebnisse

This lecture is mainly focused on the numerical simulation (using MATLAB/SIMULINK) and analog computing (using electronic circuits) of several mathematical models of Nonlinear Dynamical Systems (NDS). These models are generally expressed in forms of ordinary differential equations ODES and/or partial differential equations PDES (e.g. case of continuous NDS) or in form of coupled algebraic equations (e.g. case of discrete NDS). The ODEs and PDEs at stake are identical to those used/considered in the theoretical part of this lecture (see LV 700.371 (17W)). All ODEs and PDEs under investigation are selected in the field of engineering (e.g. in Mechanics, Electro-mechanics, Control systems, Electronics, Transportation, Telematics, etc.) as typical models of the dynamics of specific systems, scenarios, or phenomena. For each of the ODEs and PDEs models at stake, the numerical (MATLAB/SIMULINK) and experimental (ANALOG COMPUTING) studies are considered simultaneously and several numerical and experimental methods are proposed. Using these methods, numerical and experimental solutions of the mathematical models are obtained.  The proof of concepts is based on the comparison of results obtained by the three methods: (a) the analytical methods (presented in LV 700.371 (17W) Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing), (b) the numerical and (c) experimental methods (presented in this Lecture LV 700.383 (17W) LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing). The Lecture also proposes numerical methods for solving mathematical models of discrete nonlinear dynamical systems expressed in form of coupled algebraic equations. Finally numerical algorithms are developed for the analysis of oscillatory states/behavior, equilibrium states, stability, bifurcation, and chaos detection.

The general expectation regarding the knowledge to be provided/acquired is as follows:

• Mastering of numerical methods for solving linear and nonlinear ODEs and PDEs used as mathematical models of continuous nonlinear dynamical systems (CNDS).
• Mastering of the analog computing technique (i.e. use of electronic circuits) for solving nonlinear ODEs.
• Mastering of numerical methods for solving DNDS (discrete nonlinear dynamical systems).
• Mastering of numerical methods for the stability analysis of both DNDS (discrete nonlinear dynamical systems) and CNDS (continuous nonlinear dynamical systems).
• Mastering of numerical algorithms/codes for the detection of chaotic dynamics in NDS (nonlinear dynamical systems).
• Mastering of numerical algorithms/codes for bifurcation analysis in NDS.
• Mastering of the design and implementation of electronic circuits for solving nonlinear ordinary differential equations (ODEs) and Partial differential equations (PDEs).

Very Important: Many projects will be proposed in accordance to all seven points above in order to check whether the main/key objectives of this Lecture (LV 700.383 (17W)) are fulfilled. All projects proposed (by the Lecturer) are  obtained from published journal papers, which are access free through Internet (GOOGLE).

## Lehrmethodik

1. The Lecturer provides full explanation of how to write numerical codes to solve the exercises proposed in each chapter of the theoretical part of the lecture entitled: 700.371 (17W) Nonlinear Dynamics -- Modeling, Simulation and Neuro-Computing.

The following codes will be explained by the Lecturer:

Numerical codes for solving ODEs using MATLAB.

* Numerical codes for solving ODEs using SIMULINK.

Numerical codes for calculating equilibrium points.

* Numerical codes for the local stability analysis in continuous dynamical systems.

Hardware implementation of analog computers for solving nonlinear ODEs published in several journal papers. Important note: The electronic components are provided by the Lecturer. These components are available in the laboratory. Students will also find in the laboratory all necessary equipments for the achievement of their projects goals (i.e. Design and Implementation of analog computers for solving stiff ODEs and coupled ODEs).

* Numerical codes for solving discrete models.

Numerical codes for bifurcation analysis and plot/sketch of bifurcation-diagrams in continuous dynamical systems. The following types of bifurcations will be detected: Periodic- bifurcation, Period- doubling bifurcation, Quasi-periodic bifurcation, Torus bifurcation, Chaotic bifurcation, Andronov-Hopf bifurcation, Pitchfork-Bifurcation, Saddle-Node-Bifurcation, etc.

Numerical codes for  systems' states  analysis and plot of the Maximum 1D Lyapunov exponents for chaos detection in continuous dynamical systems (e.g. detection of Regular- states, Torus- states, Chaotic- states, etc).

Numerical codes for solving PDEs.

Numerical codes for solving ODES using the Cellular Neural Network paradigm.

2. Students must use the theoretical basic analytical knowledge acquired in the theoretical part of the Lecture to reproduce results published in Journal papers. These results are published in papers, which are access free through Internet (GOOGLE).

3. Students in groups of two must develop/write numerical codes to reproduce the results presented in the already published papers. The published papers are chosen by the Lecturer and, for a given topic/problem, different papers are assigned/given to each group to ensure a group will not obtain any assistance from its counterpart.

4. Numerical codes are developed by students as projects. These codes are developed in accordance to each of the chapters considered in the theoretical part of the lecture.

## Inhalt/e

Lab 1. Numerical Analysis of a Novel Four-Scroll 3D Chaotic System Using SIMULINK: Design principle of the SIMULINK graphical scheme for solving coupled nonlinear ODEs - Phase portraits - Bifurcation analysis through phase portraits

Lab 2. Numerical Analysis of a Novel Four-Scroll 3D Chaotic System Using MATLAB: Algorithms for - *Solving coupled nonlinear ODEs - *Stability of equilibrium points - *Phase portraits - *Bifurcation analysis through phase portraits

Lab 3. Analog Computing of a Novel Four-Scroll 3D Chaotic System: Design principle using electronic circuits - Phase portraits - Bifurcation analysis through phase portraits

Lab 4. Numerical solution of PDEs: MOL (Method of Lines)

Lab 5. Numerical Solution of PDEs: FDM (Finite Difference Method)

Lab 6. Numerical Solution of PDEs using Different Discretization Schemes: Discretization principle - Choice of discretization schemes - Stability of discretization schemes

Lab 7. Bifurcation Analysis of 3D Dynamical Systems: Plot of Corresponding Bifurcation Diagrams (Case1: Continuous Dynamical system - Case2: Discrete dynamical system)

Lab 8. Chaos detection in 3D Dynamical Systems: Plot of Corresponding Maximum 1D Lyapunov Exponents and detection of regular and/or chaotic states

Lab 9. Modelling and Simulation of 3D Dynamical Systems: Use of the Cellular Neural Networks (CNN) paradigm

Lab 10. Generalization of the CNN paradigm: Modelling and Simulation of Complex Nonlinear Dynamical Systems

## Erwartete Vorkenntnisse

1. Basic knowledge in MATLAB

3. Basic knowledge in Flow programming (The loops are based on following statements: if, elseif, while, do, for, etc. e.g. "for loop", "while loop", etc.).

4. Basic knowledge in Electronics

## Literatur

- Peter J. Olver, “Introduction to Partial Differential Equations,” Springer, New York, 2016

-  William E. Schiesser, and Graham W. Grifﬁths “A Compendium of Partial Differential Equation Models: Method of Lines Analysis with Matlab,” Cambridge University Press, 2006

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

- Michael Schäfer, “Computational Engineering — Introduction to Numerical Methods,” Springer, 2006

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

## Prüfungsinformationen

### Prüfungsmethode/n

1. Numerical simulation exam: Will be held at the end of the Lecture (50%)

2. Oral exam: Is held during the Lecture (this is concerned with the involvement of students into all chapters of the Lecture)(30%)

3. Projects/Homework: This measures the potential of students with regard to self-learning or learning/working autonomously (20%)

### Prüfungsinhalt/e

1. Numerical code (MATLAB) for solving stiff ODEs

2. SIMULINK graphical scheme for solving stiff ODEs and/or coupled ODEs

3. Numerical code for solving a discrete model.

4. Numerical code for solving a Partial Differential Equation (PDE).

5. Numerical code for the local stability analysis: case of a 2D dynamical system

6. Numerical code for the global stability analysis: Case of a 3D dynamical system.

7. Numerical code for Bifurcation analysis in a 3D dynamical system.

8. Numerical code for the plot of Maximum 1D Lyapunov exponent and chaos detection in a 3D dynamical system.

9. PSPICE implementation of the analog computer for solving a 3D ODE.

10. Numerical code for solving a set of 3 coupled ordinary differential equations (ODEs) using the Cellular Neural Network (CNN) technology.

### Beurteilungskriterien/-maßstäbe

1. Exercises will be proposed at the end of the Lecture to be solved numerically (this is the final exam based on:     * Numerical  simulations and/or Analog computing of ODEs and PDEs; * Numerical algorithms for chaos detection; * Numerical algorithms for bifurcation diagrams revealing the states of dynamical systems and related transitions from regular- to chaotic- states; * Numerical algorithms for equilibrium points and local stability analysis, etc.):  Duration 3 hours

2. Participation in class: Students must be  deeply involved into the Lecture by answering to questions and solving application- examples (e.g. Numerical codes for solving ODES and PDEs, Hardware implementation of electronic circuits for solving ODEs, etc. ) proposed in order to get full understand of each chapter. Several application- examples are proposed for each chapter and numerical codes are written (by students) for each application- example.

3. The self-learning potential of students will be appreciated (through Projects/Homework).

## 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)
• 700.383 LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h KS / 3.0 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)
• 700.383 LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h KS / 3.0 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)
• 700.383 LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h KS / 3.0 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)
• 700.383 LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h KS / 3.0 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)
• 700.383 LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h KS / 3.0 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)
• 700.383 LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h KS / 3.0 ECTS)

## Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung

Wintersemester 2020/21
• 700.383 KS LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)
Wintersemester 2019/20
• 700.383 KS LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)
Wintersemester 2018/19
• 700.383 KS LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)
Sommersemester 2017
• 700.383 KS LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)
Sommersemester 2016
• 700.383 KS LAB on Nonlinear Dynamics - Modeling, Simulation and Neuro-Computing (2.0h / 3.0ECTS)