Sequence of cycles and transitions to chaos in a modified Goodwin’s Growth Cycle model

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 transition to chaotic behavior via period-doubling bifurcations