An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

Abstract

This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order. The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically. In particular, the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior. Through using bifurcation diagrams, phase attractors, the maximum Lyapunov exponent and the 0–1 test, we verified that chaos exists in the new model with incommensurate fractional orders. Additionally, a complexity analysis is carried out utilizing the approximation entropy (ApEn) and C 0 complexity to prove that chaos exists. Finally, the main findings of this study are presented using numerical simulations.