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Euler equation branching; chaos; IS-LM model; QY-ML model
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.
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[2] Raines, B. E., Stockman, D. R.: Chaotic sets and Euler equation branching. J. Math. Econ. 46 (2010), 1173-1193. DOI 10.1016/j.jmateco.2010.09.004 | MR 2739547 | Zbl 1232.91467
[3] Volná, B.: Existence of chaos in plane $\mathbb{R}^2$ and its application in macroeconomics. Appl. Math. Comput. 258 (2015), 237-266. DOI 10.1016/j.amc.2015.01.095 | MR 3323066
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