**Period: 1 and 2**

**Teachers:** **dr.
Yu. A. Kuznetsov ** and ** Prof. dr.
O. Diekmann **

Info and material for the course see
THIS PAGE

We advise you to have the reader for the praktikum printed before each session,
or buy it at room WG 612(UU) for 9 euro.

**A Few Practical Remarks:**

Excercises: | Every session one can hand in the excercises, the scheme of which found below. These excercises will be graded and be part of the final grade. It is therefor advised to hand in every week. Although the computer sessions might appear as numerical analysis, do not forget that analysis is involved as well. CONTENT can be useful, but is not necessarily the only possible tool. Pencil and paper will help as well! |

Marks: |
At the last session you will be assigned a personal final project,
see also this text .
Note that after 22 december 2005 I will not mark any homework. If you still have to hand in after this date then you should contact Kuznetsov or Diekmann. |

Content: |
The software can be downloaded at THIS PAGE .
It is known that the installation may be troublesome; a few remarks in windows XP : borland installation: check that you have created two extra files, ilink32.cfg and bcc32.cfg. check that you have added the path of Borland to the Environmental variable path. or use: dummy installation manual. under linux : Check that openmotif(32 for 64-bit platforms!) is installed If you cannot use symbolic derivatives because autodiff.c cannot be compiled try to change lines like f=rneed ? "-(%s)" : "-%s"; to f= (char *) (rneed ? "-(%s)" : "-%s"); With newer versions of gcc there is a problem with __setfpucw in curve.c. We updated this file, so that the problem no longer appears. We like to hear about your difficulties and solutions! |

**Scheme :**

Date | Homework | |

15 september | section 1 & 2 | 2.7.3 Write an essay about your simulations of Langfords system |

22 september | section 3 | 3.3.3 Find a Lyapunov norm |

29 september | section 4 | 4.3.2 Find the intersection of the cusp surface with the cylinder |

6 oktober | section 5 | 5.3.3 Comparing phase portraits.(new version on www!) |

13 oktober | section 6 | 6.3.2 slow-fast motion and Excercise 3.4.6 from the lecture notes For the latter, also describe the phase portraits topologically near the equilibria. In Routh-Hurwitz: change a_{2j-i} to p_{2j-i} |

20 oktober | section 7 | 7.2.3 Bazykin, try to do more than just the numerics. |

27 oktober | section 8 | 8.4.3 (Hint: what is the symmetry group) and use 1.0/9.0 instead of 1/9 |

3 november | section 9 | 9.4.1 fold in ecology, this is a new excercise. See session IX on Kuznetsov's page. |

10 november | section 10 | 10.4.2 Bonus for analysis by hand. If in Windows you get the error message `stepsize too small', you should simply leave CONTENT, restart it and proceed. |

17 november | section 11 | 11.3.3. Study the Hopf bifurcation in the prey-predator model, both analytically and numerically. |

24 november | section 12 | 12.3.1. Study limit cycles,(can you see a symmetry?) |

1 december | section 13 | 13.2.1. Study the Hopf bifurcation. |

7 december | section 14.1 | 14.2.1. Produce a 2-parameter bifurcation diagram and compute/sketch all characteristic phase portraits.(Hint:Look for homoclinic orbits!) Note a slightly newer version is available on here . |

14 december | section 15 | NB. This is the last computer session. (See here for this session). There is no homework this time. |

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