## Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model.(English)Zbl 1363.37046

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 $$f,g: X \subset \mathbb {R}^n \rightarrow \mathbb {R}^n$$ 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.
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.

### MSC:

 37N40 Dynamical systems in optimization and economics 91B50 General equilibrium theory 91B55 Economic dynamics

### Keywords:

Euler equation branching; chaos; IS-LM model; QY-ML model
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