This course is intended to introduce the study of nonlinear-dynamical and complex systems, and a variety of applications. It should be useful to students in engineering, mathematics, or one of the sciences.
The topics covered will provide an introduction to nonlinear, complex, and disordered systems, emphasizing its concepts, ideas, and some applications. Nonlinearities often produce complex behavior,and it will be the central theme underlying the course material.
The first part of the course will focus on basic tools of dynamical systems to study nonlinear differential and difference equations with few degrees of freedom. This part includes an introduction to bifurcation theory, numerical algorithms, chaos, fractals; with many examples and applications. The last part of the course will focus on systems with many degrees of freedom, including phase transitions, critical phenomena, percolation, and also some current-research issues in spatio-temporal dynamics,collective transport in disordered systems, instabilities, and avalanches in a variety of systems.
This course will emphasize the effective use of computers in science, including interactive graphics and several useful numerical techniques. Computers can be used as a discovery tool to explore new ideas, and students will be encouraged to do so. The Science Learning Center provides the software and books needed to do most of the homeworks. Grading is based on class participation, a few homework assignements, an exam, and a class presentation.
Instructor: Prof. F. Nori, Physics Department.
S. H. Strogatz, Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry, and Engineering (Addison-Wesley, 1994);
J.H. Hubbard and B.H. West, Differential Equations: A Dynamical Systems Approach (part I and II) (Springer-Verlag, 1991 and 1995).