Abstract
The FitzHugh–Nagumo (FHN) model, from computational neuroscience, has attracted attention in nonlinear dynamics studies as it describes the behavior of excitable systems and exhibits interesting bifurcation properties. The accurate estimation of the model parameters is vital to understand how the solution trajectory evolves in time. To this end, we provide a forward sensitivity method (FSM) approach to quantify the main model parameters using sparse measurement data. FSM constitutes a variational data assimilation technique which integrates model sensitivities into the process of fitting the model to the observations. We analyze the applicability of FSM to update the FHN model parameters and predict its dynamical characteristics. Furthermore, we highlight a few guidelines for observations placement to control the shape of the cost functional and improve the parameter inference iterations.
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Acknowledgements
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number DE-SC0019290. O.S. gratefully acknowledges their support.
Data Availability
The data that supports the findings of this study are available within the article. The codes to reproduce the presented results are publicly accessible at our GitHub repository: https://github.com/Shady-Ahmed/FSM-FHN
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Ahmed, S.E., San, O., Lakshmivarahan, S. (2022). Forward Sensitivity Analysis of the FitzHugh–Nagumo System: Parameter Estimation. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81170-9_9
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