Dynamics and Bifurcations in Fractional Lozi Map

Abstract

We propose a fractional version of the Lozi map. The Lozi map is quite similar to the Henon map except that the square term of the Henon map is replaced by a linear term in the Lozi map. This map is known to be analytically tractable. The fractional version of the Lozi map displays rich dynamical behaviour. In this work, we carry out a time-series analysis of the map and present the bifurcation diagrams along with attractors for different parametric values of the map for various values of fractional order parameter (α).