Shilnikov orbits in an autonomous third-order chaotic phase-locked loop

We investigate Shilnikov homoclinic bifurcation from a new type of phase-locked loop (PLL) which uses second-order loop filter with no modulation carrier input. This system can be represented as a 3rd-order autonomous system with piecewise linear characteristics. We have found many Shilnikov orbits, and draw a bifurcation diagram in gain K/sub 0/ versus detuning /spl delta/ parameter plane.