Complex dynamics of a frequency-phase lock system

A nonlinear frequency-phase lock system with second-order filters in control circuits is considered. Dynamic states and bifurcations in this system are investigated using a dynamic model with 2.5 degrees of freedom in the cylindrical phase space. Conditions of synchronous mode stability and the locking domain boundaries are determined. The existence of various regular and chaotic asynchronous modes is revealed, and their behavior under parameter variation is studied. Results are presented using a two-parameter portrait of motions, one-parameter bifurcation diagrams, and phase portraits of attractors.