BIFURCATIONS PHENOMENA IN A NONLINEAR OSCILLATOR - APPROXIMATE ANALYTICAL STUDIES VERSUS COMPUTER-SIMULATION RESULTS

The behavior of a driven single-well oscillator with quadratic nonlinearity is studied and attention is focused on exploring a relationship between classic concepts of the approximate theory of nonlinear oscillations and the complex bifurcations and escape phenomena obtained by computer simulations. An analytical analysis of the Hill's type variational equation leads to approximate estimates for the blue-sky catastrophe and period doubling instability and eventually results in the approximate predictive criteria for the main escape region. The theoretical study and computer simulations are extended to the 1/2 subharmonic resonance and the analysis brings a new insight into the nonlinear phenomena, which occur in the higher frequency region.