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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 $\dot{x}\in \{f\left(x\right),g\left(x\right)\}$, where $f,g:X\subset {ℝ}^n\to {ℝ}^n$ are continuous and $f\left(x\right)\ne g\left(x\right)$ 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....