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Bifurcations in a class of complex differential equations

Published online by Cambridge University Press:  16 July 2009

Irene M. Moroz
Irene M. Moroz
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
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Abstract

In this paper we introduce a class of nonlinear complex ordinary differential equations that arises in the removal of channel distortion in digital telecommunication signals. Techniques from dynamical systems theory show that Hopf bifurcations are possible in the simplest of these systems. Numerical integrations, however, show that such bifurcations are degenerate. When attempts are made to follow the periodic orbits, both the period of oscillation and the principal bifurcation parameter remain fixed at their values at bifurcation. The periodic orbits exist as a family at discrete parameter values, i.e. we have a nonlinear centre. A stability régime diagram is presented

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 3 , September 1992 , pp. 273 - 282
Copyright
Copyright © Cambridge University Press 1992

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