Abstract
We generalize the two-dimensional Lozi map in order to systematically obtain piecewise 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 of the derivatives in the Lozi map.
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