NONLINEAR DYNAMICS, BIFURCATIONS AND CHAOS COURSE 777

• homework(pdf) for due date and questions assigned see "email sent to class" below

email sent to class (Text of email)

Advances in the theory of dynamical systems are penetrating many areas of science, engineering and mathematics. The qualitative aspects of this theory give a powerful way to grasp and visualise how dynamical systems work. Chaotic and bifurcation phenomena are observed in many applications and 777 should be of interest to students in engineering, physical sciences and mathematics.

777 aims to introduce graduate students to

• The powerful geometric view of the qualitative theory of dynamical systems.
• The parts of bifurcation theory most useful in applications.
• The mind-boggling chaos to be found in apparently simple systems.

 
• 777 is an interdisciplinary course open to graduate students from a wide range of departments.
 
• Prerequisites : Consent of instructor (A recommended minimum level of mathematical background is a solid knowledge of ordinary differential equations and linear algebra)
 
• Credits : 777 is a 3 credit course crosslisted in Electrical and Computer Engineering, Chemical Engineering and Mathematics.
 
• Date, time, place : 4:00 to 5:15 pm Tuesdays and Thursdays in 3444 Engineering Hall, Fall 2005. Registration call number 40759
 

• 777 was created by Ian Dobson (ECE), Michael Graham (ChE), Paul Milewski (Math), Joel Robbins (Math)
  


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• Instructor for Fall 2005: Ian Dobson
 
• If you have questions or comments for Ian: dobson@engr.wisc.edu
 
• Office hours: Wednesday 1:30-3:30 pm or by appointment in the afternoons. In addition, I am usually available just after class. e-mail is very effective for short questions. Please indicate that you are in 777 in the email because I teach another graduate class this semester.  I am NEVER available before class because I need to prepare for the class lecture. Please see Ian in person if you are having ANY difficulties with the course.
 
• Homework : There will be regular homework which will be an important part of the learning in the course. Students are encouraged to work together to solve the homework problems. However, each student must hand in their own work. Students are expected to attempt all homework problems and hand their efforts in.
 
• Project : Each student will do a project which applies or extends the course material. One objective is to link the generic course material with the students areas of interest. The project topic should be arranged with Ian, before the middle of the semester. 
 
• Background learning : The course requires a wide background and the students have diverse backgrounds. Students sometimes need to review or quickly learn unfamiliar topics to master the course material. This is encouraged and Ian will suggest supplementary reading.
 
• Assessment : The course grade is based on performance in the homework and the project. There are no exams.

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• Summary of content : Advanced interdisciplinary introduction to qualitative and geometric methods for dissipative nonlinear dynamical systems. Local bifurcations of ordinary differential equations and maps. Chaotic attractors, horseshoes and detection of chaos.
 
• syllabus
 
• reading list (pdf)
 
• poster advertising course (TeX) (pdf)
 
• Main text : Guckenheimer and Holmes, Nonlinear oscillations, dynamical systems and bifurcations of vector fields,  Applied Mathematical Sciences 42, Springer New York 1983.

• Math 561 Differential Geometry
• Math 716 Ordinary Differential Equations
• Math 819 Partial Differential Equations
• Math 820 Partial Differential Equations
• Math 821 Cellular Automata and complex random systems

Madison Chaos and Complex Systems Seminar