A novel approach to detect chaotic and periodic behaviours in fractional-order systems

This work illustrates a novel reliable test for detecting the presence of chaotic or periodic behaviours in nonlinear systems described by fractional-order differential equations. The method, which does not require phase space reconstruction of the fractional system, consists in: i) obtaining the data series, ii) constructing a random walk-type process, iii) studying how the variance of the random walk scales with time. In order to show the potentiality of the approach, the test is successfully applied to the fractional Chua, Chen and Lorenz systems.