Chaos And Nonlinear Dynamics

Overview of theoretical and numerical approaches for the study of nonlinear and chaotic dynamics in science and engineering. Fractals, bifurcation analysis, predictability, strange attractors, and routes to chaos. Roles of dissipation and noise in deterministic chaos. Use of Lyapunov spectra, fractal dimension, information, entropy, correlation functions, and attractor reconstruction to describe chaos. Chaos in iterated maps and systems of nonlinear ordinary differential equations. Spatiotemporal chaos in coupled map-lattices and in systems of nonlinear partial differential equations. Numerical integration of systems of stiff equations, operator splitting, exponential time integration, spectral and pseudo-spectral methods.