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 Affiliation||University of Alaska Anchorage|
|Keywords||discrete map, 1:2 resonance, homoclinic tangle|