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A Period-Doubling Bubble in the Dynamics of Two Coupled Oscillators

  • J. C. Alexander
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 66)

Abstract

A period-doubling cascade in the bifurcation diagram of two Brusselators coupled by diffusion is continued to a particular parameter regime, where it is seen numerically to be associated with other bifurcation branches, and in particular, “decascades;” we call the resulting bifurcation effect a period-doubling bubble. Moreover the dynamics of the bubble formation can be described. The emphasis in this note in on describing the phenomenon, although the (strong) possibility of describing it analytically in terms of unfolding a singularity which comes from interactions of singularities of the single oscillators is discussed, as well as a discussion of possibly similar behavior in other coupled oscillators.

Keywords

Hopf Bifurcation Bifurcation Diagram Unstable Manifold Homoclinic Orbit Couple Oscillator 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • J. C. Alexander
    • 1
  1. 1.Department of Mathematics and Institute for Physical Science and TechnologyUniversity of MarylandCollege ParkUSA

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