EXISTENCE OF CHAOS IN PLANE R2 AND ITS APPLICATION IN MACROECONOMICS

Abstract. The Devaney, Li-Yorke and distributional chaos in plane R2 can occur in the continuous dynamical system generated by Euler equation branching. Euler equation branching is a type of differential inclusion x ̇ ∈ {f(x), g(x)}, where f, g: X ⊂ Rn → Rn are continuous and f(x) 6 = g(x) in every point x ∈ X. Stockman and Raines in [15] defined so-called chaotic set in plane R2 which existence leads to an existence of Devaney, Li-Yorke and distributional chaos. In this paper, we follow up on [15] and we show that chaos in plane R2 with two ”classical ” (with non-zero determinant of Jacobi’s matrix) hyperbolic singular points of both branches not lying in the same point in R2 is always admitted. But the chaos existence is caused also by set of solutions of Euler equation branching which have to fulfil conditions following from the definition of so-called chaotic set. So, we research this set of solutions. In the second part we create new overall macroeconomic equilibrium model called IS-LM/QY-ML. The construction of this model follows from the fundamental macroeconomic equilibrium model called IS-LM but we include every important economic phenomena like inflation effect, endogenous money supply, economic cycle etc. in contrast with the original IS-LM model. We research the dynamical behaviour of this new IS-LM/QY-ML model and show when a chaos exists with relevant economic interpretation