  This paper examines the cycling behavior of a deterministic and a stochastic
version of the economic interpretation of the Lotka-Volterra model, the Goodwin
model. We provide a characterization of orbits in the deterministic highly
non-linear model. We then study the cycling behavior for a stochastic version,
where a Brownian noise is introduced via an heterogeneous productivity factor.
Sufficient conditions for existence of the system are provided. We prove that
the system produces cycles around an equilibrium point in finite time for
general volatility levels, using stochastic Lyapunov techniques for recurent
domains. Numerical insights are provided.
