## MTH744 |
## Dynamical Systems |

Lecturer:
Thomas Prellberg |
Semester 1, 2011/2012 |

News

- Jun 5: The 2012 exam paper is now available
- Apr 23: Revision lecture April 27, 11-12, Queens EB4. Exam May 24, 10-1
- Jan 19: A sample exam paper is now available
- Dec 15: Lecture notes are now complete
- Oct 13: Tue office hours moved to 1:30-2:30, Thu office hours moved to Fri 10:30-11:30
- Sep 24: updated module description, syllabus, and learning outcomes

Lecture times

- Thu 11-12 and 12-1, Maths room 203, starting on September 29

- Thu 3-4, Maths rooom 203, starting on October 6

- Normally Tue 1:30-2:30, Fri 10:30-11:30 in Maths B51. Please check here for up-to-date information

- Module description from the Maths UG Handbook
- Module description from the Maths PG Handbook

**Module information**

- Module syllabus
- Module objectives
- Last year's module webpage for MTH715U/MTHM021: Introduction to Dynamical Systems

- Nonlinear Dynamics and Chaos, Steven H. Strogatz, 1994

- Lecture notes to be read in connection with the textbook.

lecture | date | sections | content |
---|---|---|---|

1 | 29/9 | 1 | Introduction |

2 | 29/9 | 2.1 | One-dimensional ODEs |

29/9 | No Exercise class | ||

3 | 6/10 | 2.2-2.3 | Fixed Points and Stability |

4 | 6/10 | 2.4-2.5 | Linear Stability Analysis; Existence and Uniqueness |

6/10 | Exercise class: 2.2.8,9; 2.3.1-4; 2.4.7,8 | ||

5 | 13/10 | 2.6-2.7 | Impossibility of Oscillations; Potentials |

6 | 13/10 | 3.1 | Saddle-Node Bifurcations |

13/10 | Exercise class: 2.7.7; 3.1.2,3,5 | ||

7 | 20/10 | 3.2 | Transcritical Bifurcation |

8 | 20/10 | 3.4 | Pitchfork Bifurcation |

20/10 | Exercise class: 3.2.4,6; 3.4.2,16 | ||

9 | 27/10 | 3.6 | Imperfect Bifurcations |

10 | 27/10 | 4.1-4.3 | Flows on the circle |

27/10 | Exercise class: 3.5.8; 3.6.2; 4.3.7 | ||

11 | 3/11 | 4.4 | Flows on the circle |

12 | 3/11 | 5.1 | Two-dimensional linear flows |

3/11 | Exercise class: 4.4.4; 5.1.2,9 | ||

Reading Week: Insect Outbreak (3.7) and Fireflies (4.5) | |||

13 | 17/11 | 5.2 | Linear flows |

14 | 17/11 | 6.1 | Phase plane |

17/11 | Exercise class: 5.1.12; 6.1.3,8 | ||

15 | 24/11 | 6.2-6.3 | Phase plane (continued) |

16 | 24/11 | 6.4 | Lotka-Volterra model |

24/11 | Exercise class: 6.2.2; 6.3.4,16 | ||

17 | 1/12 | 6.5-6.6 | Conservative systems; Reversible Systems |

18 | 1/12 | 7.1 | Limit cycles |

1/12 | Exercise class: 6.5.2; 6.6.3; 7.1.3 | ||

19 | 8/12 | 7.2 | Ruling out closed orbits |

20 | 8/12 | 7.3 | Poincare-Bendixson Theorem |

8/12 | Exercise class: 7.2.6,10; 7.3.1 | ||

21 | 15/12 | 9 | The Lorenz equations and chaos |

22 | 15/12 | 9 | Chaos and strange attractors |

- A sample exam paper together with solutions is available.

Thomas Prellberg

September 2011