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

The behavior of a driven single-well oscillator with quadratic nonline arity is studied and attention is focused on exploring a relationship between classic concepts of the approximate theory of nonlinear oscill ations and the complex bifurcations and escape phenomena obtained by c omputer simulations. An analytical analysis of the Hill's type variati onal equation leads to approximate estimates for the blue-sky catastro phe and period doubling instability and eventually results in the appr oximate predictive criteria for the main escape region. The theoretica l study and computer simulations are extended to the 1/2 subharmonic r esonance and the analysis brings a new insight into the nonlinear phen omena, which occur in the higher frequency region.