Dynamics of Fractional-Order Chaotic Rocard Relaxation Econometric System

Abstract

The chaotic Rocard relaxation econometric system was proposed earlier than the Lorenz system. In this paper, the fractional-order Rocard system is investigated and its dynamical behaviors are analyzed by bifurcation diagram, Lyapunov exponent and spectral entropy (SE) complexity. The stability analysis is conducted and the conditions for the fractional-order system to maintain chaotic or periodic state are investigated. Compared with the integer-order counterpart, the fractional-order system generates more periodic parameter areas, and they play vital roles in economic cycles and economic chaos control. We also found that the fractional-order oscillator has a larger Lyapunov exponent than its integer-order counterpart. By applying the 0–1 test method, the minimum order for the system for chaotic oscillation is determined. The SE complexity evidence further confirms involving fractional calculus that enriches dynamical behaviors. These results indicate the promising applications in chaos control of the economic system.