  A classical double oscillator model, that includes in certain parameter
limits, the standard harmonic oscillator and the inverse oscillator, is
interpreted as a dynamical system. We study its essential features and make a
qualitative analysis of orbits around the equilibrium points, period-doubling
bifurcation, time series curves, surfaces of section and Poincare maps. An
interesting outcome of our findings is the emergence of chaotic behavior when
the system is confronted with a periodic force term like fcos{\omega}t.
