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Identification of two-neuron FitzHugh-Nagumo model based on the speed-gradient and filtering
1Institute for Problems in Mechanical Engineering, RAS, Saint Petersburg 199178, Russia.
Chaos (Woodbury, N.Y.)
|August 7, 2023
Summary
This study addresses parameter identification for two-neuron FitzHugh-Nagumo models with noisy membrane potential measurements and unmeasurable derivatives. A novel adaptive system using a speed-gradient method successfully estimates parameters, even with systematic sensor errors.
Area of Science:
- Computational Neuroscience
- Systems Biology
- Biophysics
Background:
- The FitzHugh-Nagumo model is a simplified representation of neuron dynamics.
- Parameter identification in neural models is crucial for understanding neuronal behavior and network function.
- Existing methods often assume ideal measurement conditions, which are not met in practice.
Purpose of the Study:
- To develop a method for parameter identification in two-neuron FitzHugh-Nagumo models.
- To address challenges posed by single-variable measurement (membrane potential), unmeasurable derivatives, and sensor noise (scaling factor).
- To account for systematic measurement errors in parameter estimation.
Main Methods:
- Transformation of the model to eliminate unmeasurable variables.
- Utilizing a second-order real filter-differentiator to approximate derivatives.
- Design of an adaptive system with parameter estimates.
- Application of the speed-gradient method for parameter estimation.
- Theoretical proof and simulation (Simulink) for validation.
Main Results:
- A novel method for parameter identification in the two-neuron FitzHugh-Nagumo model under practical measurement constraints.
- Successful estimation of model parameters despite unmeasurable derivatives and systematic sensor errors.
- Formulation and proof of sufficient conditions for asymptotically correct identification using the speed-gradient method with an integral objective function.
Conclusions:
- The proposed method offers a robust solution for parameter identification in complex neural models.
- The approach accounts for realistic measurement imperfections, enhancing applicability.
- This work paves the way for modeling and parameter estimation in larger neuron populations.
