A Proof of Chaos for a Seasonally Perturbed Version of Goodwin Growth Cycle Model: Linear and Nonlinear Formulations

We show the existence of complex dynamics for a seasonally perturbed version Goodwin growth cycle model, both in its original formulation and modified formulation, encompassing nonlinear expressions real wage bargaining function investment function. The need to deal with model is connected economically sensible position orbits, which have lie unit square, contrast what occurs model’s formulation. In proving chaos, we follow seminal idea by studying forced models economics. Namely, formulations are described Hamiltonian systems, characterized presence nonisochronous center, seasonal variation parameter, representing ratio between capital output, common frameworks, empirically grounded. Hence, exploiting periodic dependence on time that parameter enter framework Linked Twist Maps. topological results valid this context allow us prove Poincaré map, associated considered chaotic, focusing sets also when dealing model. Accordingly, trademark features chaos follow, such as sensitive initial conditions positive entropy.