Topological-numerical analysis of a two-dimensional discrete neuron model-Reference-Cited by-同舟云学术

Topological-numerical analysis of a two-dimensional discrete neuron model

Published:2023-04-01 Issue:4 Volume:33 Page:
ISSN:1054-1500
Container-title:Chaos: An Interdisciplinary Journal of Nonlinear Science
language:en
Short-container-title:

Author:

Pilarczyk Paweł¹^ORCID,Signerska-Rynkowska Justyna²³^ORCID,Graff Grzegorz³^ORCID

Affiliation:

1. Faculty of Applied Physics and Mathematics and Digital Technologies Center, Gdańsk University of Technology 1 , ul. Narutowicza 11/12, 80-233 Gdańsk, Poland

2. Dioscuri Centre in Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences 2 , ul. Śniadeckich 8, 00-656 Warszawa, Poland

3. Faculty of Applied Physics and Mathematics and BioTechMed Center, Gdańsk University of Technology 3 , ul. Narutowicza 11/12, 80-233 Gdańsk, Poland

Abstract

We conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times inside a chain recurrent set. Based on this analysis, together with the information on the size of the chain recurrent set, we develop a new method that allows one to determine subsets of parameters for which chaotic dynamics may appear. This approach can be applied to a variety of dynamical systems, and we discuss some of its practical aspects.

Funder

Narodowe Centrum Nauki

Max-Planck-Gesellschaft

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/5.0129859/16822771/043110_1_5.0129859.pdf

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