Dynamics analysis of a fractional Chaotic relaxation econometric oscillator

Abstract

In this article, a fractional Rocard's relaxation econometric oscillator is considered. Based on the fact that fractional derivatives incorporate memory factors, the integer order derivative is replaced by the Caputo fractional derivative. Stability and Hopf bifurcation conditions are obtained. Chaos in the fractional differential system is assessed by analyzing the Lyapunov characteristic exponents of the aforementioned system. Investigations show that the fractional system is chaotic and possesses similar dynamics, however, the bifurcation values differ from that of the classical system with a higher chaos occurrence probability.