Analysis and Control of a Neurodynamic Model

Abstract

Lakshmi N. Sridhar*

The dynamic interaction between Serotonin, Dopamine and Norepinephrine is very complex and nonlinear, and it is important to understand the nonlinearity and develop strategies to control the interactions effectively. In this work, bifurcation analysis and multiobjective nonlinear model predictive control are performed on a neurondynamic model involving Serotonin, Dopamine, and Norepinephrine. 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. The Hopf bifurcation point, which causes an unwanted limit cycle, is eliminated using an activation factor involving the tanh function.

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