Abstract :
Formulae for obtaining bifurcation curves of dynamical systems described by a set
of ordinary differential equations (ODE) are introduced. The plot of bifurcation curves in the
plane of characteristic parameters gives certain areas having distinguished local bifurcation
diagrams obtainable by standard tools of bifurcation theory. A trade-off between the ease of
obtaining local (but incomplete) results and the complexity of finding global diagrams is
analyzed, and a modified scheme to capture different configurations of local bifurcation
diagrams and, at the same time, obtain global results for each case of interest is proposed. This
makes it possible to explore, in a great detail, the bifurcation structure of larger regions in the
parameter plane. Briefly, the procedure consists in detecting the bifurcation curves and, in the
case of Hopf bifurcations, in calculating the stability of the emerging limit cycles. Atter that, a
detailed study by means of AUTO package is performed. The first method yields a gross
distinction among neighboring areas with different local bifurcation diagrams, while the second
method yields the global bifurcation structure in a one-parameter plot. The combined hybrid
procedure is a fast computational tool for analyzing the dynamic behaviour in general system
