Chaos and bifurcation in third-order phase locked loop

The chaos induced in a new type of phase locked loop (PLL) having a second-order loop filter is investigated. The system under consideration is modeled as a third-order autonomous system with sinusoidal phase detector characteristics. The modern nonlinear theory such as bifurcation and chaos is applied to a third-order PLL. A method is developed to quantitatively study the type of bifurcations that occur in this type of PLL. The study showed that this PLL experienced a Hopf bifurcation point as well as chaotic behaviour. The method of multiple scales is used to find the normal form near the Hopf bifurcation point. The point is found to be supercritical one.