Detecting chaos in fractional-order nonlinear systems using the smaller alignment index

The identification between chaos and ordered states in fractional-order chaotic systems is a challenge as well as a hot topic due to the complex of fractional calculus. In this paper, the smaller alignment index (SALI) is developed to detect chaos in the fractional-order chaotic systems by introducing the fractional order tangent systems. Numerical simulations are carried out based on the fractional-order simplified Lorenz system and the fractional-order Henon map, which are continuous chaotic system and discrete chaotic system, respectively. It shows that the proposed method is effective for distinguishing chaos and order in different kinds of fractional-order chaotic systems. (C) 2019 Elsevier B.V. All rights reserved.