Bifurcation sets of PLL equation with piecewise-linear PD characteristics

Abstract

In this paper we investigate the practical significance of homoclinic points in the PLL equation. We obtained parameter regions of homoclinic points in the PLL equation in our previous papers. It is well-known that if a system has homoclinic points, flows of the system present chaotic behavior at least in its transient state. We confirm this fact concretely by drawing initial condition planes for various parameter values with and without homoclinic points. As a result, it is found that for parameters without homoclinic points, the basin boundary of each attractor is smooth, however for those with homoclinic points it is more or less fractal. Further, for initial conditions chosen in fractal regions flows present chaotic transient behavior before settling in an attractor.