Work

Robust Devaney chaos in the two-dimensional border-collision normal form

Year: 2022

Type: article

Abstract: can be reduced to a four-parameter family known as the two-dimensional border-collision normal form. We prove that throughout an open region of parameter space, this family has an attractor satisfying Devaney's definition of chaos. This strengthens the existing results on the robustness of chaos in piecewise-linear maps. We further show that the stable manifold of a saddle fixed point, despite being a one-dimensional object, densely fills an open region containing the attractor. Finally, we identify a heteroclinic bifurcation, not described previously, at which the attractor undergoes a crisis and may be destroyed.

Source: Chaos An Interdisciplinary Journal of Nonlinear Science

DOI: 10.1063/5.0079807

Authors: I. Ghosh, D. J. W. Simpson

Institution: Massey University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Marsden Fund

Award: G1836917581