  Bifurcations leading to complex dynamical behaviour of non-linear systems are
often encountered when the characteristics of feedback circuits in the system
are varied. In systems with many unknown or varying parameters, it is an
interesting, but difficult problem to find parameter values for which specific
bifurcations occur. In this paper, we develop a loop breaking approach to
evaluate the influence of parameter values on feedback circuit characteristics.
This approach allows a theoretical classification of feedback circuit
characteristics related to possible bifurcations in the system. Based on the
theoretical results, a numerical algorithm for bifurcation search in a possibly
high-dimensional parameter space is developed. The application of the proposed
algorithm is illustrated by searching for a Hopf bifurcation in a model of the
mitogen activated protein kinase (MAPK) cascade, which is a classical example
for biochemical signal transduction.
