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Publication - Dr David Barton

    Stability calculations for piecewise-smooth delay equations


    Barton, D, 2009, ‘Stability calculations for piecewise-smooth delay equations’. International Journal of Bifurcation and Chaos, vol 19., pp. 639 - 650


    This paper describes a new method for computing the stability of nonsmooth periodic orbits of piecewise-smooth dynamical systems with delay. Stability computations for piecewise-smooth dynamical systems without delay have previously been performed using discontinuity mappings to `correct' the linearized period map. However, this approach is less convenient for systems with delays due to the infinite dimensional nature of the problem. Additional problems arise due to the discontinuity propagation properties of delay differential equations. The method proposed is based around a multi-point boundary value solver, which allows the correct linearized period map to be constructed directly. We present numerical examples showing the rapid convergence of the method and also illustrate its use as part of a numerical bifurcation study.

    Full details in the University publications repository