Related Experiment Video

Updated: Aug 1, 2025

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches

Published on: June 21, 2022

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

Paweł Pilarczyk¹, Justyna Signerska-Rynkowska^2,3, Grzegorz Graff³

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

Chaos (Woodbury, N.Y.)

|April 25, 2023

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.

More Related Videos

Quantitative Analysis of Neuronal Dendritic Arborization Complexity in Drosophila

Quantitative Analysis of Neuronal Dendritic Arborization Complexity in Drosophila

Published on: January 7, 2019

Analyzing Dendritic Morphology in Columns and Layers

Analyzing Dendritic Morphology in Columns and Layers

Published on: March 23, 2017

Related Concept Videos

Neuron Structure

Neuron Structure

Neurons are the main type of cell in the nervous system that generate and transmit electrochemical signals. They primarily communicate with each other using neurotransmitters at specific junctions called synapses. Neurons come in many shapes that often relate to their function, but most share three main structures: an axon and dendrites that extend out from a cell body.
Structure and Function of Neurons
The neuronal cell body—the soma— houses the nucleus and organelles vital to...

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Articles linked to this work by shared authors, journal, and citation graph.

Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model.

Chaos (Woodbury, N.Y.)·2026

Rigorous computation of expansion in one-dimensional dynamics.

Chaos (Woodbury, N.Y.)·2025

Analysis of dynamics of a map-based neuron model via Lorenz maps.

Chaos (Woodbury, N.Y.)·2024

Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices.

Chaos (Woodbury, N.Y.)·2023

Persistent homology as a new method of the assessment of heart rate variability.

PloS one·2021

See all related articles