Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model

summary:We focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion $\dot x \in \{f(x),g(x)\}$, where $f,g\colon X \subset \mathbb {R}^n \rightarrow \mathbb {R}^n$ are continuous and $f(x)\neq g(x)$ at every point $x \in X$. It seems this chaotic behaviour is typical for such dynamical system. \newline In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called the IS-LM model