MA 605 - Introduction to Nonlinear Dynamics (3-0-0)

Instructor: Dr. P.S. Dutta

Nonlinear equations: autonomous and non-autonomous systems, phase portrait, stability of equilibrium points, Lyapunov exponents, periodic solutions, local and global bifurcations, Poincare-Bendixon theorem, Hartmann-Grobmann theorem, Center Manifold theorem.

Nonlinear oscillations: perturbations and the Kolmogorov-Arnold-Moser theorem, limit cycles. Chaos: one-dimensional and two-dimensional Poincare maps, attractors, routes to chaos, intermittency, crisis and quasi periodicity. Synchronization in coupled chaotic oscillators. Applications: Examples from Biology, Chemistry, Physics and Engineering.

Schedule: Lectures on Monday, Tuesday, Wednesday.