Ultimate Boundedness and Finite Time Stability for a High Dimensional Fractional-Order Lorenz Model

Abstract

In this paper, the global attractive set (GAS) and positive invariant set (PIS) of the five-dimensional Lorenz model with the fractional order derivative are studied. Using the Mittag-Leffler function and Lyapunov function method, the ultimate boundedness of the proposed system are estimated. An effective control strategy is also designed to achieve the finite time stability of this fractional chaotic system. The corresponding boundedness and control scheme are numerically verified to show the effectiveness of the theoretical analysis.

Keywords

• the Mittag-Leffler GAS
• five-dimensional Lorenz model
• Mittag-Leffler stability
• finite time stability