Analysis and Control of the Hodgkin-Huxley Model
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Abstract
Objective: The Hodgkin-Huxley model is one of the most influential mathematical models in neuroscience, describing how electrical activity is generated and propagated in neurons. In this work, bifurcation analysis and Multiobjective Nonlinear Model Predictive Control are performed on the dynamic Hodgkin-Huxley model.
Methods: The MATLAB program MATCONT was used to perform the bifurcation analysis. The MNLMPC calculations were performed using the optimization language PYOMO in conjunction with the state-of-the-art global optimization solvers IPOPT and BARON.
Results: The bifurcation analysis revealed the existence of Hopf bifurcation points and limit points. The MNLMC converged on the Utopian solution. Hopf bifurcation points, which cause unwanted limit cycles, are eliminated using an activation function based on the tanh function.
Conclusion: The limit points (which cause multiple steady-state solutions from a singular point) are very beneficial because they enable the Multiobjective Nonlinear Model Predictive Control calculations to converge to the Utopia point (the best possible solution) in the model. The tanh activation function is highly effective at eliminating Hopf Bifurcations.
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Copyright (c) 2026 Sridhar LN.
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