A dynamical system is any system whose state changes as a function of time. This course studies the regular and irregular behaviour of nonlinear dynamical systems, concentrating on ordinary differential equations (ODEs) and their solutions.

Topics from the theory of ODEs include: existence and uniqueness theorems; linear ODEs with constant and periodic coefficients and Floquet theory; linearization and stability analysis; perturbation methods; bifurcation theory; phase plane analysis for autonomous systems. The theory is illustrated with applications to physical, biological and ecological systems.

In addition, a selection from the dynamical concepts: Hamiltonian dynamics, resonant oscillations, chaotic systems, Lyapunov exponents, Poincare maps, homoclinic tangles.