Analysis and Control of the Improved Denatured Morris-Lecar Neuron Model

Abstract

Lakshmi N. Sridhar*

The dynamics of neurons is very complex and nonlinear, and it is important to understand the nonlinearity and develop strategies to control mechanisms as effectively as possible. In this work, bifurcation analysis and multiobjective nonlinear model predictive control is performed on the Improved Denatured Morris-Lecar Neuron Model. Bifurcation analysis is a powerful mathematical tool used to deal with the nonlinear dynamics of any process. Several factors must be considered, and multiple objectives must be met simultaneously. 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. The bifurcation analysis revealed the existence of a Hopf bifurcation point and a limit point. The MNLMC converged to the utopia solution. The Hopf bifurcation point, which causes an unwanted limit cycle, is eliminated using an activation factor involving the tanh function. 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.

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