Keywords
limit cycle
equilibrium state
Hopf bifurcation theorem
modelo de control optimal bi-dimensional
ciclo límite
estado de equilibrio
teorema de bifurcación de Hopf
How to Cite
Abstract
This paper deals with one of the most important public health problem in the whole world that is diabetes, and more precisely its complications. From a model examining the complications or not of a population of diabetics, we associate a nonlinear optimal control problem. Considering the previous, we prove that the equilibrium state exists and is a saddle point. Moreover, we claim the unexistence of limit cycle in such a population, which is an interesting result concerning this world evil. Then we give some examples for which we characterize the equilibrium state which is not necessarily admissible.
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