Nonlinear Dynamic Systems

3 units

State space and functional analysis approaches to nonlinear systems. Questions of existence, uniqueness, and stability; Lyapunov and frequency-domain criteria; w-limits and invariance, center manifold theory and applications to stability, steady state response and singular perturbations. Poincare-Bendixson theory, the van der Pol oscillator and the Hopf Bifurcation theorem.