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Computation of normal form coefficients of cycle bifurcations of maps by algorithmic differentiation

Author

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  • Pryce, J.D.
  • Khoshsiar Ghaziani, R.
  • De Witte, V.
  • Govaerts, W.

Abstract

As an alternative to symbolic differentiation (SD) and finite differences (FD) for computing partial derivatives, we have implemented algorithmic differentiation (AD) techniques into the Matlab bifurcation software Cl_MatcontM, http://sourceforge.net/projects/matcont, where we need to compute derivatives of an iterated map, with respect to state variables. We use derivatives up to the fifth order, of the iteration of a map to arbitrary order. The multilinear forms are needed to compute the normal form coefficients of codimension-1 and -2 bifurcation points. Methods based on finite differences are inaccurate for such computations.

Suggested Citation

  • Pryce, J.D. & Khoshsiar Ghaziani, R. & De Witte, V. & Govaerts, W., 2010. "Computation of normal form coefficients of cycle bifurcations of maps by algorithmic differentiation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 109-119.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:1:p:109-119
    DOI: 10.1016/j.matcom.2010.07.014
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