@article{38626,
  keywords = {arnold horns, hopf bifurcation, invariant, parametric degeneracy, resonance},
  author = {BB PECKHAM and Frouzakis and Kevrekidis},
  title = {BANANAS AND BANANA SPLITS - A PARAMETRIC DEGENERACY IN THE HOPF-BIFURCATION FOR MAPS},
  abstract = { The set of Hopf bifurcations for a two-parameter family of maps is typically a curve in the parameter plane. The side of the curve on which the invariant circle exists is further divided by horn-shaped resonance regions, with each region corresponding to maps that have a periodic orbit of a certain period. With the presence of a parametric degeneracy, the resonance regions sometimes take the form of closed {\textquoteright}{\textquoteright}bananas{\textquoteright}{\textquoteright} instead of open-ended horns. The authors investigate this local codimension-two bifurcation, emphasizing resonance regions as projections to the parameter plane of surfaces in phase x parameter space. The authors present scenarios where the degeneracy occurs {\textquoteright}{\textquoteright}naturally{\textquoteright}{\textquoteright} and illustrate them through an adaptive control application. More global implications of the local study are also discussed. },
  year = {1995},
  journal = {Siam Journal on Mathematical AnalysisSiam Journal on Mathematical Analysis},
  volume = {26},
  pages = {190-217},
  month = {01/1995},
  isbn = {0036-1410},
  language = {English},
}