Work

Multilevel regularity of orbits of expanding Lorenz maps with application to the Courbage-Nekorkin-Vdovin model

Year: 2025

Type: article

Abstract: We discuss the structure and properties of itineraries of periodic orbits for expanding Lorenz maps with nontrivial rotation interval. In particular, it is shown that periodic orbits of such maps are organized in two cascades (called Stern-Brocot and Geller-Misiurewicz cascades), which are closely related to the Farey tree of rational rotation numbers of a given map. The obtained results are illustrated with a reduced Courbage-Nekorkin-Vdovin neuron model, allowing us to characterize regularity of periodic spiking patterns in the model.

Source: Discrete and Continuous Dynamical Systems - B

DOI: 10.3934/dcdsb.2025076

Authors: Piotr Bartłomiejczyk, Piotr Nowak-Przygodzki, Justyna Signerska-Rynkowska

Institution: Gdańsk University of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Narodowym Centrum Nauki

OpenAlex ID: W4410327402

FWCI: 1.7

Cites: 21

Cited by: 1

Related to: 10