A higher-dimensional generalization of the Lozi map: Bifurcations and dynamics

Abstract

We generalize the two dimensional Lozi map in order to systematically obtain piece-wise continuous maps in three and higher dimensions. Similar to higher-dimensional generalizations of the related Hénon map, these higher-dimensional Lozi maps support hyperchaotic dynamics. We carry out a bifurcation analysis and investigate the dynamics through both numerical and analytical means. The analysis is extended to a sequence of approximations that smooth the discontinuity in the Lozi map.