Chaos and bifurcation in time delayed third order phase-locked loop

In this paper, the modern nonlinear theory is applied to a third order phase locked loop (PLL) with feedback time delay. Due delay, different behaviors that are not accounted for in conventional PLL model identified, namely, oscillatory instability, periodic doubling and chaos. Firstly, Pade approximation used delay where it utilized deriving state space representation of under investigation. The consideration simulated without It shown certain gain (control parameter) values, system changes its stability becomes chaotic. Simulations show chaotic control parameter value less than one i.e, stable region narrower. Moreover, wider as increases.