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Professor Alan Champneys

Professor Alan Champneys

Professor Alan Champneys
B.Sc.(Birm.), D.Phil.(Oxon.)

Professor of Applied Non-linear Mathematics

Office 2.58 MVB
Merchant Venturers Building,
Woodland Road, Clifton BS8 1UB
(See a map)

+44 (0) 117 331 5606
+44 (0) 117 331 5643


  • 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.


Brief Career History

  • 1985-1988 BSc. in Mathematics, University of Birmingham Graduated with first class honours.
  • 1988-1991 PhD. in Mathematics, Wadham College University of Oxford. Thesis title The nonlinear dynamics of articulated pipes conveying fluid, supervisor T. Brooke Benjamin FRS.
  • 1992-1993 Postdoctoral Research Assistant in the School of Mathematical Sciences, University of Bath sponsored by the EPSRC (formerly SERC) on Numerical computation of invariant manifold bifurcations. Jointly supervised by John Toland and Alastair Spence .
  • 1993- Lecturer in Nonlinear Systems. Department of Engineering Mathematics, University of Bristol. Reader since 1998. Professor since 2001.
  • 1997-2002 EPSRC Advanced Fellowship


Nonlinear dynamics and chaos and its application, particularly to engineering systems. Bifurcation theory, i.e. understanding abrupt changes from regular to complex dynamics. Application to rotor dynamics, aircraft bridges, flow-induced oscillation, parametric resonance in general including stabilisation 'upside down'. The theory of how continuous enterties give rise to localised response. For example, solitary waves, localised buckling patterns and 'kinks' or dislocations in atomic lattices. A unifying mathematical description of such phenomena, and dedicated computational techniques. Solitary waves in nonlinear optics. Localised pulses of light, so-called 'light bullets'. The mechanics of rods, such as helical buckling of cables, pipelines and DNA strands. Dynamics of piecewise systems, such as impacts, switches and backlash.

  • chaos
  • resonance
  • localisation
  • nonlinear dynamics
  • solitary wave
  • dynamics of impact
  • engineering instability
  • Memberships


    Department of Engineering Mathematics

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