A Bayesian estimation of unfolded pitchfork bifurcation structure based upon experimental data

We consider the practical problem of estimating parameter values for the unfolding of a pitchfork bifurcation from observed data. Although the existence of a bifurcation point may have been theoretically determined, observed data from experiments or measurement must reflect the natural unfolding due to existing perturbations and imperfections. We demonstrate how a Bayesian approach provides a natural formulation to this problem and how incremental observations alter our best assessment of the true, unfolded, bifurcation structure, close to the prior estimate (the pitchfork). This method may be useful in practice to estimate the location of bifurcation branches other than a particular one experimentally observed. © The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.