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. In the last three decades, various discrete models of a single neuron were introduced, aimed at reflecting the dynamics of neural processes. Unfortunately, analytical methods offer limited insight into the nature of some phenomena encountered by such models. In this paper, we study the classical multi-parameter Chialvo model by means of a novel topological method that uses set-oriented rigorous numerics combined with computational topology. We enrich the existing tools with a new approach that we call finite resolution recurrence. We obtain a comprehensive picture of global dynamics of the model, and we reveal its bifurcation structure. We combine the recurrence analysis with machine learning methods in order to detect parameter ranges that yield chaotic behavior.
Authors
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1063/5.0129859
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2023
