Title: Single Element Nonlinear Chimney Model,
Abstract: We generalize the chimney model by introducing nonlinear restoring and
gravitational forces for the purpose of modeling swaying of trees at high wind
speeds. Here we have restricted to the simplest case of a single element and
the governing equation we arrive at has not been studied so far. We study the
onset of fractal basin boundary of the two fixed points and also observe the
chaotic solutions. We also examine the need for considering the full sine term
in the gravitational force.