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Bifurcation theory is the usual analytic approach to study the parameterspace of a dynamical system. Despite the great power of prediction of thesetechniques, fundamental limitations appear during the study of a given problem.Nonlinear dynamical systems often hide their secrets and the ultimate resourceis the numerical simulations of the equations. This paper presents a method toexplore bifurcations by using the basin entropy. This measure of theunpredictability can detect transformations of phase space structures as aparameter evolves. We present several examples where the bifurcations in theparameter space have a quantitative effect on the basin entropy. Moreover, sometransformations, such as the basin boundary metamorphoses, can be identifiedwith the basin entropy but are not reflected in the bifurcation diagram. Thecorrect interpretation of the basin entropy plotted as a parameter extends thenumerical exploration of dynamical systems.

Using the basin entropy to explore bifurcations