Analysis and Control of Brain Dynamic Models

Abstract

Lakshmi. N. Sridhar

The nonlinear behavior of the brain's information processing represents one of the key tasks in modern neuroscience, and a lot of research has been conducted in trying to rhythmicity in brain networks. 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. Bifurcation analysis and multi objective nonlinear model predictive control (MNLMPC) calculations are performed on two brain dynamic models. 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 Hopf bifurcation points that lead to limit cycles in the two models. These Hopf points were eliminated using an activation factor that involves the tanh function. The multi objective nonlinear model predictive control calculations converge to the Utopia point in both the problems, which is the best solution.

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