151-0532-00L  Nonlinear Dynamics and Chaos I

SemesterSpring Semester 2014
LecturersG. Haller
Periodicityyearly recurring course
Language of instructionEnglish


AbstractBasic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics.
ObjectiveThis course is intended for Masters and Ph.D. students in engineering sciences, physics and applied mathematics who are interested in the behavior of nonlinear dynamical systems. It offers an introduction to the qualitative study of nonlinear physical phenomena modeled by differential equations or discrete maps. We discuss applications in classical mechanics, electrical engineering, fluid mechanics, and biology. A more advanced Part II of this class is offered every other year.
Content(1) Basic facts about nonlinear systems: Existence, uniqueness, and dependence on initial data.

(2) Near equilibrium dynamics: Linear and Lyapunov stability

(3) Bifurcations of equilibria: Center manifolds, normal forms, and elementary bifurcations

(4) Nonlinear dynamical systems on the plane: Phase plane techniques, limit sets, and limit cycles.

(5) Time-dependent dynamical systems: Floquet theory, Poincare maps, averaging methods, resonance

(6) Chaotic dynamics: Homoclinic dynamics, attractors, Lyapunov exponents
Lecture notesThe class lecture notes will be posted electronically after each lecture. Students may rely on these or prepare their own notes during the lecture.
Prerequisites / NoticeThe course will be given in English.

- Prerequisites: Analysis and a basic course in differential equations.

- Exam: two-hour on-line exam in English.

- Homework: A homework assignment will be due roughly every other week. Solutions will be posted after the homework due dates.

- Grade policy: Up to 10% of the final grade is given for turning in all homework assignments before their due dates. An additional 15% of the final grade is based on one randomly selected homework, which will be graded at the end of the semester. The remaining 75% of the final grade is based on the exam.