Deficits and cycles
The paper presents two simple examples of nonlinear macro-economic cycle models in which a Hopf bifurcation may occur at a critical point in a real-valued model parameter interval. The underlying model is characterized by functions \(A_{\mu}\), \(\phi_{\mu}\), \(k_{\mu}\), indexed by a real parameter \(\mu\) : \(A_{\mu}(t+1)=A_{\mu}(\phi_{\mu}(R(t))\), \(R(t+1))\), \(k_{\mu}(t+1)=k_{\mu}(R(t+1))\), where \(A_{\mu}(t)\) represents asset demand at time t, R(t) represents the gross real rate of asset returns between time t-1 and time t, and \(k_{\mu}(t)\) represents capital demand by firms. Competitive equilibria are the solutions to the difference equation \(A_{\mu}(t+1)-k_{\mu}(t+1)=R(t)(A_{\mu}(t)-k_{\mu}(t))\), with certain initial conditions.
scientific article; zbMATH DE number 3980854