Transitions from localization to nonlocalization in strongly nonlinear damped oscillators

We present an analysis to study transition from localization to nonlocalization due to damping in a strongly nonlinear oscillator. This is performed by computing separate analytical approximations for the early (localized) and late (nonlocalized) response of the system, and then matching these approximations at a transition point. Satisfactory agreement between the theoretical results and those derived by direct numerical integrations of the equations of motion is noted. Due to the structure of the localized modes of the system under consideration, this analysis can be viewed as a passage through bifurcation study.