A.S. Gorobtzov, E.N. Ryzhov, A.S. Churzina

One of the basic problem of biomedical technologies is change of characteristics and adjust of rhythms to the processes proceeding in live organisms. The considered mechanism allows to control not only amplitude of a rhythm, but also possibility of switching on other mode. In this connection tendencies recently were outlined in construction of the general concept of biological rhythms. One of applied problems of dynamics of rhythms is control of geometry of a profile of a rhythm that, in particular, is connected with control of amplitudes of processes of Lame. Typical classification of rhythms is defined by the linked system of oscillatory with certain type of general general nonlinearity. In the article the problem about bifurcation of rhythm of Lame is considered. As a result bifurcation the rhythm of Lame is switched from one self-oscillatory mode to another that corresponds to an exchange of stability between limit cycles. The decision of the problem leads to consideration of layers in phase space with invariant borders which are the closed manifolds. In the case of a phase plane the mechanism of bifurcation defines an exchange of stability between limit cycles. The approach to construction of mechanisms of supervision is based on the theory of synthesis integrated asymptotically stable manifolds in spaces of conditions: Construction of function of Lyapunov leads to synthesis of the observer which registers stabilization of system in a vicinity of border of area.