Chaos in a quartic dynamical model

We study the orbital characteristics of a time independent, two dimensional quartic dynamical model with two exact periodic orbits that displays always closed zero velocity curves. It is shown that the stability of the periodic orbits depends on the value of the coupling parameter . Computer calculations suggest that the degree of stochasticity is small for the values of in the range 1<<3 while it grows rapidly when >3. We also compute the Lyapunov characteristic exponents for different values of the coupling parameter.