Modified function projective lag synchronization in fractional-order chaotic (hyperchaotic) systems

Abstract

In this paper, a novel modified function projective lag synchronization (MFPLS) for fractional-order chaotic (hyperchaotic) systems is proposed. Considering fractional derivatives do not satisfy the Leibniz product rule, as it is known in integer-order calculus, it is difficult to achieve the synchronization with a scaling function between the drive and response systems in the time domain. In this paper, we construct the equivalent integer-order systems based on the Laplace transform and make numerical calculation. By means of the Lyapunov stability theory, an adaptive controller is designed to achieve MFPLS for the transformed systems. According to the mapping relationship between the original and transformed systems, MFPLS for the fractional-order chaotic systems is achieved. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.