Bifurcation transitions in dynamic systems of pulse voltage regulator

In this article bifurcations in nonlinear dynamical systems are considered and special attention is paid to bifurcations-crises, which are identified with catastrophes in systems. The qualitative change in the phase portrait that occurs when the parameter m of the system changes is called the bifurcation of the phase portrait. The value of the system parameter m = m0, at which bifurcation occurs, is called the bifurcation value of the parameter (or bifurcation point). Mathematical models are presented in unsaturated mode; in saturation mode. Sufficient conditions are given under which the Andronov-Hopf bifurcation takes place. Quantitative relations are determined for the conditions under which the Andronov-Hopf bifurcation takes place in the system. Numerical values of parameters are entered, at which the system takes a quite compact, but quite informative form.