Chaos and Statistical Methods pp 161-166 | Cite as

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

Conference paper

## Abstract

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

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

(1)

## Keywords

Librium Point Strange Attractor Ordinary Differential Equation Stable Limit Cycle Stable Equilibrium Point
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## References

- Y. Ueda: IEEE 24th Midwest Symposium on CAS Proc., pp. 549–553 (1981)Google Scholar
- Y. Ueda: J. Statistical Physics, 20, 2, pp. 181–196 (1979)MathSciNetADSCrossRefGoogle Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1984