AN EFFECTIVE METHOD FOR DETECTING CHAOS IN FRACTIONAL-ORDER SYSTEMS

This paper illustrates a reliable binary test for detecting the presence of chaos in nonlinear systems described by fractional-order differential equations. The method, which is inspired by the technique proposed in [Gottwald & Melbourne, 2004] for integer-order differential equations, does not require phase space reconstruction of the fractional system. It consists of obtaining the data series, constructing a random walk-type process and studying how the variance of the random walk scales with time. In order to show the capabilities of the approach, the test is successfully applied to three well-known dynamical systems, i.e. fractional Chua, Chen and Lorenz systems.