Modêlos não lineares do sistema respiratório

Abstract

This work is based on the mathematical of the respiratory system, in which not only a law of the proportional plus derivative type is proposed, but also the concept of singular points of the types, saddle and unstable focus, to form the limit cycle to explain the behaviour cyclical of the system. Maintaining the characteristics of the original model we define the parameter of the controller, using the nbtion of a bifurcation of the type stable focus to unstable focus, obtaining then a stable limit-cycle, whose amplitude was determined analitically by the method of Krylov-Bogoliubov-Mitropolsky (KBM). The frequency of the oscillatory solution defined in the original model as being the frequency of the respiration, decrease initially when we increase the concentration of the inhaled CO2 (CICO2). This initial decrease is incoherent with reality. When we introduced in the original model the effect of circulation time of the venous and arterial bloods, we verified that in the case of a humoural: control, the identification wasn't viable to real circulation time. Having verified these facts we proposed a new model, where the respiratory rithimicity is elaborated in the respiratory center, by the action of an oscillatory signal. This signal is different from the signal that comes from the controller system refered to above, but it maintains with the controller system signal an interdependence so that the frequency and the amplitude of the respiratory oscillation are influenced by the controller signal.