A filtered H\'enon map
Dynamical Systems
2022-12-01 v1 Signal Processing
Chaotic Dynamics
Abstract
In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the H\'enon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic or not, depending on the filter coefficients. The dynamics of the system presents complex behavior, including cascades of bifurcations, coexistence of attractors, crises, and "shrimps". The obtained results are relevant in the context of bandlimited chaos-based communication systems, that have recently been proposed in the literature.
Cite
@article{arxiv.2211.16964,
title = {A filtered H\'enon map},
author = {Vinícius S. Borges and Marcio Eisencraft},
journal= {arXiv preprint arXiv:2211.16964},
year = {2022}
}
Comments
Final version published in Chaos, Solitons & Fractals (2022)