Parameter Estimation of the Network of FitzHugh-Nagumo Neurons Based on the Speed-Gradient and Filtering
The paper addresses the problem of parameter estimation (or identification) in dynamical networks composed of an arbitrary number of FitzHugh-Nagumo neuron models with diffusive couplings between each other. It is assumed that only the membrane potential of each model is measured, while the other state variable and all derivatives remain unmeasured. Additionally, potential measurement errors in the membrane potential due to sensor imprecision are considered. To solve this problem, firstly, the original FitzHugh-Nagumo network is transformed into a linear regression model, where the regressors are obtained by applying a filter-differentiator to specific combinations of the measured variables. Secondly, the speed-gradient method is applied to this linear model, leading to the design of an identification algorithm for the FitzHugh-Nagumo neural network. Sufficient conditions for the asymptotic convergence of the parameter estimates to their true values are derived for the proposed algorithm. Parameter estimation for a network of five interconnected neurons is demonstrated through computer simulation. The results confirm that the sufficient conditions are satisfied in the numerical experiments conducted. Furthermore, the algorithm's capabilities for adjusting the identification accuracy and time are investigated. The proposed approach has potential applications in nervous system modeling, particularly in the context of human brain modeling. For instance, EEG signals could serve as the measured variables of the network, enabling the integration of mathematical neural models with empirical data collected by neurophysiologists.
Code (0)
등록된 구현이 없습니다.
Tasks
EEGparameter estimationMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Equilibrium Propagation and Hamiltonian Inference in the Diffusive Fitzhugh-Nagumo Model
In this work, we extend the Equilibrium Propagation framework to skew-gradient systems and show an equivalence between deep Energy-Based Models and Hamiltonian neural networks. We focus on networks of diffusively coupled…
Quantifying wave propagation in a chain of FitzHugh-Nagumo neurons
Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly u…
Time SeriesSubthreshold signal encoding in coupled FitzHugh-Nagumo neurons
Despite intensive research, the mechanisms underlying how neurons encode external inputs remain poorly understood. Recent work has focused on the response of a single neuron to a weak, subthreshold periodic signal. By si…
Simplified models of pacemaker spiking in raphe and locus coeruleus neurons
Many central neurons, and in particular certain brainstem aminergic neurons exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz. A large number of ion channel types contribute to such spikin…
Parameter Estimation with Dense and Convolutional Neural Networks Applied to the FitzHugh-Nagumo ODE
Machine learning algorithms have been successfully used to approximate nonlinear maps under weak assumptions on the structure and properties of the maps. We present deep neural networks using dense and convolutional laye…
parameter estimationTime Series Analysis