TY - JOUR

T1 - On adaptive parameters identification of Hindmarsh–Rose neuron models

AU - Kovalchukov, A.

AU - Fradkov, A.

N1 - Export Date: 01 November 2025; Cited By: 0; Correspondence Address: A. Kovalchukov; Institute for Problems of Mechanical Engineering Russian Academy of Sciences, St-Petersburg, 61 Bolshoy Ave V. O., 199178, Russian Federation; email: koaa@ipme.ru; CODEN: CSFOE

PY - 2025/8/5

Y1 - 2025/8/5

N2 - This publication is devoted to the exploration of the Hindmarsh–Rose model, a biological neuron model that provides a good balance between complexity and variability. We focus on the model parameter identification problem, which is a critical aspect of control system theory. The complexity of the problem arises from the presence of numerous nonlinear functions and a large number of unknown parameters. The following sub-issues are covered in this work. The first subtopic explores the Hindmarsh–Rose model parameters identification problem with measurable output. In address this problem, we develop an algorithm based on the Speed Gradient method. We establish the necessary conditions for obtaining precise estimates and prove the corresponding theorem. The second subtopic is devoted to the network identification problem, which involves two non-identical Hindmarsh–Rose models. We propose an identification algorithm capable of estimating both the model parameters and the coupling strength. Furthermore, we provide a mathematical proof demonstrating that, under certain conditions, the algorithm converges reliably. We also illustrate both problems with numerical simulations. © 2025 Elsevier B.V., All rights reserved.

AB - This publication is devoted to the exploration of the Hindmarsh–Rose model, a biological neuron model that provides a good balance between complexity and variability. We focus on the model parameter identification problem, which is a critical aspect of control system theory. The complexity of the problem arises from the presence of numerous nonlinear functions and a large number of unknown parameters. The following sub-issues are covered in this work. The first subtopic explores the Hindmarsh–Rose model parameters identification problem with measurable output. In address this problem, we develop an algorithm based on the Speed Gradient method. We establish the necessary conditions for obtaining precise estimates and prove the corresponding theorem. The second subtopic is devoted to the network identification problem, which involves two non-identical Hindmarsh–Rose models. We propose an identification algorithm capable of estimating both the model parameters and the coupling strength. Furthermore, we provide a mathematical proof demonstrating that, under certain conditions, the algorithm converges reliably. We also illustrate both problems with numerical simulations. © 2025 Elsevier B.V., All rights reserved.

KW - Adaptive identification

KW - Biological neural network

KW - Hindmarsh–Rose model

KW - Identification problem

KW - Network identification

KW - Neural dynamics

KW - Nonlinear dynamics

KW - Speed-Gradient algorithm

KW - Control theory

KW - Dynamics

KW - Gradient methods

KW - Neural network models

KW - Neurons

KW - Biological neural networks

KW - Hindmarsh-Rose model

KW - Model parameter identifications

KW - Neuron modeling

KW - Parameter identification problems

KW - Speed-gradient algorithms

KW - Parameter estimation

UR - https://www.mendeley.com/catalogue/2320f807-fa51-3626-85ba-7e234c76f4ab/

U2 - 10.1016/j.chaos.2025.116815

DO - 10.1016/j.chaos.2025.116815

M3 - статья

VL - 200

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -