Can derivative determine the dynamics of fractional-order chaotic system?

Abstract

Dynamics, control and applications of fractional-order systems are important issues in nonlinear science, and have received increasing interests in recent years. However, most of the existing studies are carried out based on the constant order fractional (COF) nonlinear systems. Moreover, there are few publications on bifurcation, chaos, complexity of variable order fractional (VOF) nonlinear systems. In this paper, variable fractional derivative orders such as periodical signal, noise signals are introduced into the fractional-order Simplified Lorenz chaotic system. Numerical solution, LEs, complexity measuring algorithms are proposed, and how the dynamics can be changed by the variable orders is discussed in detail. The results indicate that the dynamics of the VOF can be controlled by the designed variable orders and the VOF Simplified Lorenz system has higher complexity than its COF counterpart. The results demonstrate the effectiveness and advantages of the proposed method and the engineering application worth of the VOF systems.