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

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...

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Bibliographic Details
Published in:Journal of difference equations and applications 2023-12, Vol.29 (9-12), p.982-993
Main Authors: Bilal, Shakir, Ramaswamy, Ramakrishna
Format: Article
Language:English
Subjects:
Bifurcations
hyperchaos
Piecewise smooth map
smooth approximation
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Summary: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.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2022.2041625