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

2020/05/04 by Shakir Bilal, Bilal, Shakir, Ramakrishna Ramaswamy +1
Computer Science · Mathematics · Physics and Astronomy · #Chaos-based Image/Signal Encryption #Mathematical Dynamics and Fractals #Chaos control and synchronization

paper · pdf · doi:10.48550/arxiv.2005.01849

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 Henon 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.

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