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

  • Y. Ueda
  • H. Ohta
Part of the Springer Series in Synergetics book series (SSSYN, volume 24)

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).

Keywords

Librium Point Strange Attractor Ordinary Differential Equation Stable Limit Cycle Stable Equilibrium Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Y. Ueda
    • 1
  • H. Ohta
    • 1
  1. 1.Department of Electrical EngineeringKyoto UniversityKyotoJapan

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