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

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.

Keywords:

• Piecewise smooth map
• hyperchaos
• smooth approximation

2020 Mathematics Subject Classifications:

• 37M05
• 39A28

Acknowledgments

S. B. would like to thank UGC (Govt of India) for support. S. B. and R. R. designed the study. S. B. performed the analysis. S. B. and R. R. wrote the manuscript. All authors read and approved the final manuscript.

Disclosure statement

The authors declare no conflict of interest.

Additional information

Funding

R. R. is supported by the DST (Govt of India) through the JC Bose fellowship.