Work

Discrete Lorenz attractors of new types in three-dimensional maps with axial symmetry

Year: 2024

Type: article

Abstract: We propose a new class of quadratic three-dimensional maps with the axial symmetry and constant Jacobian that is additional to the well-known class of quadratic three-dimensional Hénon maps. We study dynamical properties and bifurcations in three-parameter families of these axial symmetric maps and show that such maps can have discrete Lorenz attractors, including those of new types in which one-dimensional unstable separatrices of a saddle fixed point are twisted. We also demonstrate typical scenarios that start with a stable fixed point and lead to the appearance of discrete Lorenz attractors of various types. Additionally, we show numerically that such attractors can be robustly chaotic, i.e. they preserve the maximum Lyapunov exponent to be positive for all smooth perturbations. • A new class of 3D quadratic maps with the axial symmetry is presented. • Two main normal forms of such maps with constant Jacobian are constructed. • Discrete Lorenz attractors of various types are described and their examples are shown. • Homoclinic structures of discrete Lorenz attractors of twisted type are illustrated. • Pseudohyperbolic properties of the attractors are studied.

Source: Partial Differential Equations in Applied Mathematics

DOI: 10.1016/j.padiff.2024.100904

Authors: S.V. Gonchenko, A.S. Gonchenko

Institutions: National Research University Higher School of Economics, N. I. Lobachevsky State University of Nizhny Novgorod

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,230

Funders: Ministry of Education and Science of the Russian Federation, Russian Science Foundation, Lobachevsky State University of Nizhny Novgorod