Modeling and Characterization of a Fractional Lorenz Chaotic Variant with the Infinite State Representation

In this paper, the infinite state representation is applied to model a fractional variant of the Lorenz chaotic system. Thanks to a finite dimension approximation, the original fractional order system is converted into a large dimension set of integer order nonlinear differential equations whose initial conditions permit to test the sensitivity of the equivalent chaotic system. This sensitivity is quantified thanks to Lyapunov exponents which are computed with an experimental technique and the Gram-Schmidt algorithm.