Condition of generation of oscillations in dynamic system with nonlinear periodical functions

The authors present the results of research by qualitative methods of the theory of differential equations and modeling of one class of toroidal systems. Systems with two periodical nonlinear functions that are systems with a toroidal phase surface are studied. The phase portrait is shown on the torus surface, because the mathematical model has two periodical functions. It is specified that in nonlinear dynamic systems with a toroidal phase surface the exact fronts of the region of oscillation existence are defined by two bifurcations.<>