https://doi.org/10.1140/epjp/s13360-024-05438-y
Regular Article
Pathways to hyperchaos in a three-dimensional quadratic map
School of Digital Sciences, Digital University Kerala, 695317, Pallipuram, India
Received:
26
April
2024
Accepted:
8
July
2024
Published online:
20
July
2024
This paper deals with various routes to hyperchaos with all three positive Lyapunov exponents in a three-dimensional quadratic map. The map under consideration displays strong hyperchaoticity in the sense that in a wider range of parameter space, the system showcases three positive Lyapunov exponents. It is shown that the saddle periodic orbits eventually become repellers at this hyperchaotic regime. By computing the distance of the repellers to the attractors as a function of parameters, it is shown that the hyperchaotic attractors absorb the repelling periodic orbits. First, we discuss a route from stable fixed point undergoing period-doubling bifurcations to chaos and then hyperchaos and role of saddle periodic orbits. We then illustrate a route from doubling bifurcation of quasiperiodic closed invariant curves to hyperchaotic attractors. Finally, the presence of weak hyperchaotic flow-like attractors is discussed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
