Tools
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.
Matlab code examples
Svends new codes by 12 March 2016:
Lin_Analysis_1D_GUI_SDJ.m
Lorentz_SDJ.m
Svends new code by 5 April 2018:
PhasePot_2D_GUI_SDJ.m
Reading, Exercises and Solutions
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.[14], 2.2.[17;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.[34], 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.[12;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;45;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
Solutions: 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
Solutions: Solution
 Friday 2.3, kl. 1011
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 PointcareBendixon Theorem). Find such a region (hint: try with a square). Also do ex: 7.6.[5;9], 8.1.6
Solutions: 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.
Solutions: 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
Solutions: 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
Solutions: 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
 Friday 23.3, 911, Aud. A
Exercises: Exam 2014, Exam 2015,
Exam 2016

Wednesday 4.4, 10:1512:00
Jonas is available for questions regarding exercises, Aud A, NBI

Monday 9.4, 10:1512:00
Question hour for Exam, Aud. 8, HCO
 Wednesday 11.4
Written Exam: 913