On the Effect of Mutually Coupled Autonomous Chaotic Third-Order Phase-Locked Loop

A third order Phase locked loop, PLL, is widely used in communication systems. Lately, researcher had found that under certain conditions, such as gain, PLL is experiencing chaotic oscillations. For a single PLL, studies have shown that when the gain of PLL increases, it will encounter a chaotic behavior. To see the mutual effect of two coupled PLL, this paper will derive the mathematical dynamical model and use the modern nonlinear theory to investigate the chaotic oscillations. Chaotic signal could be generated from mutually coupled PLL the coupling gives a wide chaotic region and a robust one if intended to be use for chaos generation, also the coupling value vary the region of stability, here in this paper we demonstrate this by computer simulation.