Strange Attractors in a System Described by Nonlinear Differential-Difference Equation

Abstract

This report deals with strange attractors which occur in a system described by the following differential-difference equation:

$$\frac{{d\theta (t)}}{{dt}} + \sin \theta (t - L) = \delta$$

((1))

. This equation is a mathematical model of phase-locked loops (PLL) with time delay. Synchronized states of the PLL are represented by the equilibrium points of the equation. The pull-in region, i.e., the parameter region in which all initial conditions lead to quiescent steady states, was already reported with some regions correlated with asynchronized steady states [1]. This report surveys various types of steady states, especially chaotic steady states, in computer-simulated systems of Eq. (1).