RECONSTRUCTING BIFURCATION DIAGRAMS ONLY FROM TIME-WAVE-FORMS

A simple algorithm is proposed for ''reconstructing'' bifurcation diag rams only from time-waveforms of a dynamical system, without knowing a n explicit form of the dynamics and its dependence on the parameters. Reconstruction means that the obtained bifurcation diagram is qualitat ively similar to that of the original system. The algorithm consists o f two steps. First, a nonlinear predictor is sought using a particular class of functions with many parameters. Second, the Karhunen-Loeve t ransform is used to find only significant parameters contributing the bifurcations. The algorithm is tested against two families of dynamica l system: the Henon family and the coupled logistic/delayed-logistic f amily.