Dynamics of a Modified Third–Order Phase–Locked Loops (PLL): Melnikov Approach, Simulations

In this article, we investigate the dynamics of new modified third-order Phase-Locked Loops (PLLs). Our goal here is to investigate the effect of the new factor ∑j=1Najsin(jωt) on the dynamics of the proposed model. Using perturbation techniques based on Andronov–Melnikov concepts, we demonstrate that horseshoe chaos exists in three-dimensional nonautonomous systems. Several simulations are performed. Additionally, we present a few specific modules for examining the dynamics of the hypothetical oscillator circuit under consideration. This will be a crucial component of a much broader web-based scientific computing application. We will explicitly note that the proposed model is hypothetical and specialists working in this scientific field have a say. We will consider a numerical example of the possible application of the Melnikov function in the modeling of the radiation Melnikov antenna diagram. In addition, we examine a generalization based on probability distributions.