Analysis of the dynamics of a two-dimensional Hindmarsh

Title	Analysis of the dynamics of a two-dimensional Hindmarsh–Rose neuron model
Authors	O. S. Kostromina¹ ¹National Research Lobachevsky State University of Nizhny Novgorod
Annotation	Using known methods of qualitative theory and bifurcation theory of dynamic systems on a plane, an analytical and numerical analysis of the dynamics of a two-dimensional Hindmarsh–Rose neuron model is carried out depending on its parameters. A bifurcation diagram is constructed on the plane of control parameters. Bifurcation curves, some of which are obtained analytically, some of which are obtained numerically, divide the plane of parameters into thirteen regions with different topologies of phase portraits, which are established for each obtained region.
Keywords	Hindmarsh–Rose model, limit cycles, bifurcations.
Citation	Kostromina O. S. ''Analysis of the dynamics of a two-dimensional Hindmarsh–Rose neuron model'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 114-118. Available at: https://conf.svmo.ru/files/2025/papers/paper23.pdf. - Date of access: 30.08.2025.