Parametric study of the fractional-order Chen–Lee system

The dynamics of fractional-order systems have attracted a great deal of attention in recent years. In this paper, the effects of parameter changes on the dynamics of the fractional-order Chen–Lee system were studied numerically. The parameter ranges used were relatively broad. The order used for the system was fixed at 2.7 (q1 = q2 = q3 = 0.9). The system displays rich dynamic behaviors, such as a fixed point, periodic motion (including period-3 motion), chaotic motion, and transient chaos. The chaotic motion identified was validated by the confirmation of a positive Lyapunov exponent. Period-doubling routes to chaos in the fractional-order Chen–Lee system were also found.