Scaling symmetry of the Hodgkin-Huxley mathematical model

Authors

Vladimir Valerievich Galanin, Samara State Medical UniversityFollow

Abstract

A computational method based on the application of a scaling transformation to the Hodgkin-Huxley mathematical model of the biological neuron and its generalizations to the case of various neural systems is proposed. The method makes it possible: 1) to obtain invariants of the scaling transformation of the Hodgkin-Huxley model; 2) to find self-similarity regions corresponding to the modes of neural activity; 3) to determine the conditions for the similarity of models of various types of biological neurons; 4) to reduce the order of the system of differential equations of the Hodgkin-Huxley model for neural systems with synchronous activity. The capabilities of the method are demonstrated using various examples from neurobiology.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

DOI

https://doi.org/10.13023/psmij.2025.06-01-02

Recommended Citation

Galanin, Vladimir Valerievich (2025) "Scaling symmetry of the Hodgkin-Huxley mathematical model," Progress in Scale Modeling, an International Journal: Vol. 6: Iss. 1, Article 2.
DOI: https://doi.org/10.13023/psmij.2025.06-01-02
Available at: https://uknowledge.uky.edu/psmij/vol6/iss1/2