We focus on the special type of the continuous dynamical system which is genWe 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 ˙x ∈ {f(x), g(x)}, where f, g : X ⊂ ℝ n → ℝ n are continuous and f(x) ≠ g(x) at every point x ∈ 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.