SEQUENCES OF CYCLES AND TRANSITIONS TO CHAOS IN A MODIFIED GOODWIN'S GROWTH CYCLE MODEL
Abstract
The model introduced by Goodwin [1967] in "A Growth Cycle" represents a milestone in the nonlinear modeling of economic dynamics. On the basis of a few simple assumptions, the Goodwin Model (GM) is formulated exactly as the well-known Lotka–Volterra system, in terms of the two variables "wage share" and "employment rate". A number of extensions have been proposed with the aim to make the model more robust, in particular, to obtain structural stability, lacking in GM original formulation. We propose a new extension that: (a) removes the limiting hypothesis of "Harrod-neutral" technical progress: (b) on the line of Lotka–Volterra models with adaptation, introduces the concept of "memory", which plays a relevant role in the dynamics of economic systems. As a consequence, an additional equation appears, the validity of the model is substantially extended and a rich phenomenology is obtained, in particular, transition to chaotic behavior via period-doubling bifurcations.
