Browse/search for people

Professor Alan Champneys

  • Applied dynamical systems

    . Understanding complicated dynamics (e.g. chaos) in physical systems governed by ordinary or partial differential equations in terms of bifurcation theory. Global bifurcations (homoclinic and heteroclinic orbits). Bifurcations (grazing and sliding) unique to piecewise-smooth systems. Parametric resonance; the `Indian Rope trick'. Application across engineering to aircraft and structural dynamics, power electronics, fluid-structure interaction.

  • Numerical bifurcation theory

    . Path-following; use of the codes AUTO and CONTENT. Numerical analysis of homoclinic and heteroclinic bifurcations, including homoclinic orbits to periodic orbits, numerical branch-switching and stability calculations. Algorithms for periodic orbits of large systems.

  • Localised phenomena

    . Existence theories for multiplicities of homoclinic orbits in Hamiltonian and reversible systems. Applications to nonlinear elastic buckling. Localised buckling of cylinders , rods and struts. Solitary waves in suspension bridges. Applications to solitary water waves with surface tension, and generalised solitary waves (homoclinics to periodics). Applications to nonlinear optics; "embedded" solitons, second-harmonic generation, optical parametric oscillators. Localised modes of higher-oder continuum models for lattice equations.