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.