Course homepage: http://www.ipr.umd.edu/~wlosert/phys715/
 

Professor:    Wolfgang Losert	Email:          wlosert@glue.umd.edu
Office:             A.V. Williams  Rm 3359	Office phone:  405-0629
Lab:                Energy Research Bldg Rm 0101	Lab phone:      405-6759

Lecture    M, W 3:00-4:15 pm  in Phys 1219.
Office hours: after class, or email/drop by

Suggested Textbooks:

        Ott, Chaos in Dynamical Systems
        Strogatz, Nonlinear Dynamics and Chaos

Nonlinear terms enter into equations for many systems, e.g. the weather, lasers, fluids, or biological systems.  The dynamics of such systems can be very complex, often with a very sensitive dependence on the chosen initial conditions (an indication of chaos).  Still many - often surprisingly general - principles can be used to describe nonlinear dynamics and chaos.  This course will cover the theoretical foundations, numerical techniques, and some current applications of chaos and nonlinear dynamics.  Covered topics include strange attractors, Lyapunov exponents, quasiperiodicity, period doubling, intermittency, crises, fractal basin boundaries, chaotic scattering, KAM tori, and quantum chaos.  Applications include pattern formation, chaos control, and synchronization.

Homework is due each Monday at 6pm, in my mailbox in AV Williams Room 3322

A paper about a current topic in nonlinear Dynamics and Chaos must be submitted at the end of the semester.  The topic can be chosen from any field where nonlinear dynamics plays an important role.  Please discuss your paper topic with me.  You may choose to address the topic as a theoretical problem, or through simulations.  Additional credit is given for web-posting of papers.  The paper will include a brief in class presentation and discussion of the topic.

There will be two take-home exams: One midterm and one final comprehensive exam.

Midterm:    15%
Final exam:    20%
Homework and class participation:     30%
Paper:     35%
Homework turned in late will receive less credit. You will receive 2/3 credit if the work is turned in within one week of the due date, and 1/3 credit if it is turned in before the end of classes.

 

Week	Class	Reading	Notes
Jan 28	Introduction, Linear and nonlinear ODE's	Chapter 1 Ott Chapter 1 Strogatz
Feb 4	1D flows	parts of Chapter 2-4 Strogatz
Feb 11	2D flows	parts of Chapter 5,6 Strogatz
Feb 18	Bifurcations and Limit Cycles	parts of  Chapter 7,8 Strogatz
Feb 25	Chaos and Maps	parts of Chapter 9,10 Strogatz Chapter 2 Ott
Mar 4	Fractals and Strange attractors	parts of Chapter 11,12 Strogatz Chapter 3 Ott
Mar 11	Tools and Measures	Chapter 4 Ott
Mar 18	Midterm (DUE Apr 1)
Mar 25	Spring Break
Apr 1	Time series analysis / Chaos control	Chapter 4 Ott / Abarbanel book	paper topic due (April 3)
Apr 8	Nonattracting Chaotic Sets	Chapter 5 Ott	paper outline due (DUE Apr 10)
Apr 15	Hamiltonian Chaos	Chapter 7 Ott
Apr 22	Chaotic transitions	Chapter 8 Ott
Apr 29	Multifractals / Synchronization	Ch 9 Ott
May 6	Higher dimensional systems / Patterns
May 13	Pattern Formation		Last class May 13
May ??	Final exam		paper due