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.