Some complex differential equations arising in telecommunications

  • Irene M. Moroz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1463)


The control equations describing the removal of distortion from a transmitted digital signal are complex nonlinear coupled ordinary differential equations in real time. The simplest of the class of such equations is studied for its bifurcation structure, by a combination of analytical and numerical techniques. We find that Hopf bifurcations are possible, but the limit cycles exist only at bifurcation. Actual data is used in numerical integrations. When parameters are chosen which are appropriate to the telecommunications context, all fixed points are stable and no Hopf bifurcations occur.


Hopf Bifurcation Main Pulse Bifurcation Structure Telecommunication Engineer Simple Analytical Formula 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. W. Lucky (1966), Bell Syst. Tech. J. 45, 255.CrossRefGoogle Scholar
  2. [2]
    I. M. Moroz, S. A. Baigent, F. M. Clayton and K. V. Lever (1989), "Bifurcation Analysis of the Control of an Adaptive Equaliser" Submitted to IEEE.Google Scholar
  3. [3]
    J. Guckenheimer and P. Holmes (1983), "Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields" Springer-Verlag, Berlin.CrossRefzbMATHGoogle Scholar
  4. [4]
    K. V. Lever and I. M. Moroz (1989), "Modelling the Control of Complex Adaptive Equalisers with Carrier Recovery Phase-Locked Loop. GEC Internal Report.Google Scholar
  5. [5]
    I. M. Moroz, G. J. McCaughan and K. V. Lever, "Bifurcations in Standard and Series Equalisers" In Preparation.Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Irene M. Moroz

There are no affiliations available

Personalised recommendations