Existence of chaos in the plane R2 and its application in macroeconomics

The Devaney, Li-Yorke and distributional chaos in the plane R2 can occur in the continuous dynamical system generated by Euler equation branching. Euler equation branching is a type of differential inclusion ẋ∈{f(x),g(x)}, where f,g:X⊂Rn→Rn are continuous and f(x)≠g(x) in every point x∈X. Stockman and Raines (2010) defined the so-called chaotic set in the plane R2 whose existence leads to the existence of Devaney, Li-Yorke and distributional chaos. In this paper, we follow up on Stockman and Raines (2010) and we show that chaos in the plane R2 is always admitted for hyperbolic singular points in both branches not lying in the same point in R2. But the chaos existence is also caused by a set of solutions of Euler equation branching. We research this set of solutions. In the second part we create the new overall macroeconomic equilibrium model called IS-LM/QY-ML model. This model is based on the fundamental macroeconomic equilibrium model called IS-LM model. We model an inflation effect, an endogenous money supply, an economic cycle etc. in addition to the original IS-LM model. We research the dynamical behaviour of this new IS-LM/QY-ML model and show when a chaos exists with relevant economic interpretation.