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

Area of Science:

• Computational neuroscience
• Dynamical systems theory
• Topological data analysis

Background:

• The Chialvo neuron model (1995) is a foundational two-dimensional model for studying neuronal dynamics.
• Set-oriented topological methods offer rigorous analysis of global dynamics in complex systems.

Purpose of the Study:

• To develop a new computational method for identifying parameter subsets that induce chaotic dynamics.
• To analyze return times within chain recurrent sets for dynamical systems.
• To apply and discuss the practical aspects of this novel approach for parameter space exploration.

Main Methods:

• Computer-assisted analysis of the Chialvo two-dimensional neuron model.
• Application of a set-oriented topological approach for global dynamics analysis.
• Development of a new algorithm for analyzing return times within chain recurrent sets.

Main Results:

• A novel method is established for determining parameter subsets associated with chaotic dynamics.
• The size of the chain recurrent set is integrated into the parameter identification process.
• The approach demonstrates applicability to various dynamical systems beyond the neuron model.

Conclusions:

• The developed method provides a robust framework for detecting chaotic dynamics in parameter spaces.
• This research contributes to a deeper understanding of neuronal excitability and complex system behavior.
• The methodology offers practical tools for analyzing and predicting chaotic regimes in diverse scientific fields.