## MTH744 |
## Dynamical Systems |

Lecturer:
Thomas Prellberg |
Semester 1, 2012/2013 |

News

- May 28: this year's exam paper.
- Nov 15: student questionnaire results
- Sep 26: room change on Sept 27: Maths 513 instead of Maths 203

Lecture times

- Thu 11-12 and 12-1, Maths room 203, starting on September 27

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

- Normally Thu 1:30-2:30 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 MTH744U/MTH744P: 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 | 27/9 | 1 | Introduction |

2 | 27/9 | 2.1 | One-dimensional ODEs |

27/9 | No Exercise class | ||

3 | 4/10 | 2.2-2.3 | Fixed Points and Stability |

4 | 4/10 | 2.4 | Linear Stability Analysis |

4/10 | Exercise class: 2.2.8,9; 2.3.1,3; 2.4.7,8 | ||

5 | 11/10 | 2.5-2.7 | Existence and Uniqueness; Impossibility of Oscillations; Potentials |

6 | 11/10 | 3.1 | Saddle-Node Bifurcations |

11/10 | Exercise class: 2.6.2; 2.7.7; 3.1.2 | ||

7 | 18/10 | 3.2 | Transcritical Bifurcation |

8 | 18/10 | 3.4 | Pitchfork Bifurcation |

18/10 | Exercise class: 3.1.5; 3.2.4,6; Sample Exam Question 1 | ||

9 | 25/10 | 3.6 | Imperfect Bifurcations |

10 | 25/10 | 4.1-4.3 | Flows on the circle |

25/10 | Exercise class: 3.4.2,16; 3.5.8; 3.6.2 | ||

11 | 1/11 | 4.4 | Flows on the circle |

12 | 1/11 | 5.1 | Two-dimensional flows |

1/11 | Exercise class: 4.3.7; 4.4.4; 5.1.2,9 | ||

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

13 | 15/11 | 5.1 | Linear flows |

14 | 15/11 | 5.2 | Classification of Linear Flows |

15/11 | Exercise class: any of 5.2.3-10; 5.1.12 | ||

15 | 29/11 | 6.2-6.3 | Phase plane |

16 | 29/11 | 6.4 | Lotka-Volterra model |

29/11 | Exercise class: 6.1.3, 6.2.2; 6.3.4,16 | ||

17 | 6/12 | 6.5-6.6 | Conservative systems; Reversible Systems |

18 | 6/12 | 7.1 | Limit cycles |

6/12 | Exercise class: 6.5.2; 6.6.3; 7.1.3 | ||

19 | 13/12 | 7.2 | Ruling out closed orbits |

20 | 13/12 | 7.3 | Poincare-Bendixson Theorem |

13/12 | Exercise class: 7.2.6,10; 7.3.1 |

- A sample exam paper together with solutions is available, also last year's exam paper.

Thomas Prellberg

September 2012