Dynamics of the driven Goodwin business cycle equation

We study dynamics of the Goodwin nonlinear accelerator business cycle model with periodic forced autonomous investment Ia(t) = a(1 – cos ωt), where a and ω are the amplitude and the frequency of investment. We give examples of the parameters a and ω when the chaotic oscillations of income are possible. We find the critical values of amplitude acr (ω): if a > acr (ω) the period of the income equals to the driving period T=2π/ω.