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

2023/04/01 by Paweł Pilarczyk, Justyna Signerska‐Rynkowska, Justyna Signerska-Rynkowska +1
Neuroscience · Physics and Astronomy · #Chaos control and synchronization #Neural dynamics and brain function #stochastic dynamics and bifurcation

paper · doi:10.1063/5.0129859

openalex publication_date 2023/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Citations

• MAP BASED MODELS IN NEURODYNAMICS
• A quantitative description of membrane current and its application to conduction and excitation in nerve
• Modeling of spiking-bursting neural behavior using two-dimensional map
• A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
• Simple model of spiking neurons

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