1:2 Resonance Bifurcation in the E-I Map

Bifurcation and Continuation

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1:2 Resonance Bifurcation in the E-I Map

The movie comprises a sequence of phase portraits of the E-I map in the vicinity of the codimension 2 point of a 1:2 resonance bifurcation occurring on a period 2 orbit as a parameter is varied. Each phase portrait is composed of two orbits, with transient dynamics denoted by the light-colored iterates and the long-term dynamics denoted by dark-colored iterates. The sequence of bifurcations leads to the formation of a pair of double homoclinic tangles, only one of which is shown. 

For details of the E-I map and the 1:2 resonance see the reference: 

S. E. Folias & G. B. Ermentrout, Spatially localized synchronous oscillations in synaptically coupled neuronal networks: conductance–based models and discrete maps.
SIAM J. Appl. Dyn. Syst. 9 (2010), pp. 1019-1060 

Author Institutional AffiliationUniversity of Alaska Anchorage
Author Email
Keywordsdiscrete map, 1:2 resonance, homoclinic tangle

Documents to download

  • Mp4 of 1:2 Resonance(.mp4, 111.55 MB) - 640 download(s) The movie comprises a sequence of phase portraits of the E-I map in the vicinity of the codimension 2 point of a 1:2 resonance bifurcation occurring on a period 2 orbit as a parameter is varied. Each phase portrait is composed of two orbits, with transient dynamics denoted by the light-colored iterates and the long-term dynamics denoted by dark-colored iterates. The sequence of bifurcations leads to the formation of a pair of double homoclinic tangles, only one of which is shown.

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