Hidden Boundary of Global Stability in a Counterexample to the Kapranov Conjecture on the Pull-In Range

Within the framework of the development of the theory of hidden oscillations, the problem of determining the boundary of global stability and revealing its hidden parts corresponding to the nonlocal birth of hidden oscillations is considered. For a phase-locked loop with a proportional-integrating filter and a piecewise-linear phase detector characteristic, effective methods for determining bifurcations of global stability loss, for obtaining analytical formulas for bifurcation values, and for constructing trivial and hidden parts of the global stability boundary are suggested.