## MATH 722 Nonlinear Dynamics and Chaos II, Spring 2017

**Lectures: ** 9:30am-10:45am, Monday and Wednesday in

TBD (

map) unless otherwise noted on the schedule below.

**Syllabus:** Click here to download (PDF). (

*Updated 8 Feb 2017*)

**Office Hours:** 11-12 Mon and 12:30-1:30pm Weds in 220 DMSC, or by appointment.

**Textbook:** Kuznetsov, Yuri.

*Elements of Applied Bifurcation Theory* (3rd). [

Review]

**Website:** This course uses

**WebCampus (https://wcl.unr.edu)** in addition to the instructor's website for the course at

http://www.pauljhurtado.com/teaching/SP17/.

# Tentative Schedule

Week | Monday | Wednesday | Notes |

1: Jan 23, 25 | Introduction & overview | Linear ODEs & Review | Notes: All |

2: 1/30, 2/1 | Basic Definitions and Examples | (continued) | Ch. 1 Notes: All |

3: Feb 6, 8 | Smale Horseshoe and Shift Maps | ODEs and Poincare Maps | Ch. 1 Notes: M.B. |

4: Feb 13, 15 | Topological Equivalence of Systems | Generic types of equilibria; Bifurcations | Ch. 2 Notes: Z.H. |

5: Feb 20, 22 | NO CLASS (Presidents Day) | One-parameter Bifurcations (continuous) | Ch. 3 Notes: A.R. |

6: Feb 27, 3/1 | One-parameter Bifurcations; Normal Forms | One Parameter Bifurcations; Structural Stability; Center Manifolds (Intro) | Ch. 3 Notes: W.V. |

7: Mar 6, 8 | One-parameter Bifurcations (discrete) | Discuss Projects; Center Manifolds | Ch. 4-5 Notes: M.B. |

8: Mar 13, 15 | Center Manifolds | Discuss Projects | Ch. 5; Notes: Z.H. |

9: Mar 20, 22 | NO CLASS | NO CLASS | Spring Break |

10: Mar 27, 29 | Center Manifolds: Local Approximation | (continued) | Ch. 6; First Project Proposal Due Notes: A.R. |

11: Apr 3, 5 | Other Bifurcations | (continued) | Ch. 7-9; Notes: W.V. |

12: Apr 10, 12 | (continued) | (continued) | Ch. 7-9 Notes: M.B. |

13: Apr 17, 19 | TBD | TBD | Project Draft Due Notes: Z.H. |

14: Apr 24, 26 | TBD | TBD | Notes: A.R. |

15: May 1, 3 | TBD | TBD | Notes: W.V. |

16: May 8 | Project Presentations & Write-up Due | Dead Day | |