Computer programs useful for the analysis of dynamical systems include

- MATLAB. You are covered by a KU site license. To obtain MATLAB for a local installation, go to punkt.ku.dk, click on "Software" and follow the instructions from there.
- Mathematica. NBI has a campus license which also coverse private laptops of students. You can download an installation image from our servers and install it on your local machine. For detailed instructions, please see this page.

Svends new codes by 12 March 2016:

PhasePot_2D_GUI_SDJ.m

Lin_Analysis_1D_GUI_SDJ.m

Lorentz_SDJ.m

Please find below a rough outline of the course by date. In order to be prepared for the lectures and exercise sessions, please read the chapters and try to solve the problems indicated for a given lecture.

We will upload the solutions for each week's exercises after each exercise session. Be aware that they may be filled with mistakes. If you spot a mistake, please inform us.

Last time of update: 2017.20.12.

**Monday 05.2**

Chaos and fractals; flows on the line (until 2.3) (Chapter 1,2)

NOTE: No exercises on the 5th.

**Wednesday 07.2**

Bifurcations in 1D (Chapters 2 and 3)

Exercises: 2.1.[1-4], 2.2.[1-7;11], 2.3.2.

Slides: Slide Hints

Solutions: Solution**Monday 12.2**

Bifurcations and Circle systems (Chapter 3, 4)

Exercises: 2.4.[1;4;7], 2.5.[3-4], 2.6.2 and 2.7.6

Solutions: Solution**Wednesday 14.2**

Linear systems in 2D (Chapter 5 without subchapter 5.3)

Exercises: 3.1[1;3], 3.2.[2;4;5], 3.4.[1;3;14], 3.5.8

Solutions: Solution**Monday 19.2**

Phase plane (Chapter 6 without subchapter 6.8)

Exercises: 4.1.[1-2;8], 4.3.1, 5.1.[1,9], 5.2.[2,4,11,12]

Solutions: Hints Solution**Wednesday 21.2**

Limit cycles (Chapter 7 without subchapter 7.4)

Exercises: 6.1.[2;5], 6.3.[1;4-5;8;14] and possibly matlab exercises

Solutions: Hints(Updated) Solution**Monday 26.2**

Lecture moved to Friday 2.3

Exercises: 6.5.[1;11;13], 6.3.10, 6.6.7

Solution**Wednesday 28.2**

MATLab (Svend Steffensen) (**NOTE: Lecture starts 10.30)**

HUSK din LAPTOP !

Exercises: 6.8.[2;4], 7.2.[6;10], 7.3.4

Solution**Friday 2.3, kl. 10-11**

Nonlinear Oscillations (Chapter 7)

**Monday 05.3**

Nonlinear Oscillations (Chapter 7)

Exercises: Look at ex. 7.3.4. again. Since there exists a closed orbit in the phase plane you should be able to find a*''trapping region''*,**R**(The Pointcare-Bendixon Theorem). Find such a region (hint: try with a square). Also do ex: 7.6.[5;9], 8.1.6

Solution**Wednesday 07.3**

2d Bifurcations, Hopf bifurcations (Chapter 8 withour subchapter 8.4 and 8.5) and Lorenz Equations (Chapter 9)

Exercises: 8.2.1, 8.2.9, 8.3.1, 8.7.1

Use Svends code "PhasePot_2D_GUI_SBS.m" for help.

Solution**Monday 12.3**

Lorenz Equations (Chapter 9) and 1D maps (Chapter 10)

Exercises: 9.1.4, 9.2.1, 9.2.6, 9.4.2

Solution**Wednesday 14.3**

1D maps and period doubling (Chapter 10 without subchapter 10.7)

Exercises: 10.1.10, 10.1.12, 10.3.2, 10.3.10

Solution**Monday 19.3**

Fractals (Chapter 11)

Exercises: 10.4.3, 10.5.1, 11.2.1, Exam 2000 ex III, 8.4.5

Exam 2000

Solution Also refer to the solutions to Exam 2000 in the exam archive.**Wednesday 21.3**

Strange attractors (Chapter 12 without subchapter 12.5) and what do we do in 'Biocomplexity' (Jonas S. Juul)

Exercises: 11.3.8, 11.4.2, 8.2.3 and Exam 2004 ex II

Exam 2004, Exam 2013

Solution**Monday 26.3**

Exercises: Exam 2014, Exam 2015, Exam 2016

Thursday 30.3, 10:15-12:00

- 11.4

Written Exam: 9-13