Abstract

BERNARD, Séverine; CESAR, Ténissia; NUIRO, Silvère P.  and  PIETRUS, Alain. Unexistence of limit cycle in an optimal control problem of a population of diabetics. Rev. Mat [online]. 2018, vol.25, n.2, pp.239-259. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v25i2.33692.

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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.

Keywords : two-dimensional optimal control model; limit cycle; equilibrium state; Hopf bifurcation theorem.

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