A Period-Doubling Bubble in the Dynamics of Two Coupled Oscillators
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.
KeywordsHopf Bifurcation Bifurcation Diagram Unstable Manifold Homoclinic Orbit Couple Oscillator
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