Chaos from orbit-flip homoclinic orbits generated in a practical circuit.

A new class of chaotic systems is generated in a practical, nonlinear, mutually coupled phase-locked loop (PLL) circuit. Theoretical results make it possible to understand experimental results of such PLL's on the onset of chaos using the geometry of the invariant manifolds, while the resultant simple geometry and complex dynamics is expected to have applications in other areas, e.g. , power systems or interacting bar magnets. The 1D map projected from a numerically obtained attractor indicates the existence of a piece-wise linear structure having a sensitive dependence on the bifurcation parameter fo2.