Business Cycles and Torus in the Non-homogeneous Multiplier-Accelerator Model

Abstract

This paper analyzes the well known multiplier-accelerator model from a mathematical point of view. It introduces non-linear components to standard linear models. Using the theory of normal forms, the existence of the stable non-homogeneous invariant torus has been shown.

Keywords

• non-linear second-order differential equation
• periodic solution
• invariant torus
• theory of normal forms
• multiplier-accelerator model
• non-homogeneous model
• hopf's bifurcation
• landau's scenario for turbulence
• non-linear dynamics