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Estimating the escape zone for a parametrically excited pendulum-type equation

This paper derives theoretical results for determining bifurcation curves which provide bounds on anticipated "escape" regimes in a two-dimensional parameter space for an equation which is a natural extension of a commonly used second-order parametrically excited nonlinear pendulum equation. An application of these results is made for an equation which often arises in smectic liquid-crystal problems. The results for this application are more refined yet qualitatively similar to those obtained by different methods reported in the literature.