MS#54. The double cusp, 1989
With Gottfried Mayer-Kress, Alex Keith, and Matthew Koebbe
Int. J. Bifurcations and Chaos, 1(2):417-430 (March, 1991)
Subjects: Bifurcation theory
Written: October 26,1989
Abstract: In 1975, Isnard and Zeeman proposed a cusp catastrophe model for the polarization of a social group, such as the population of a democratic nation. Ten years later, Kadyrov combined two of these cusps into a model for the opinion dynamics of two "non-socialist" nations. This is a non-gradient dynamical system, more general than the double cusp catastrophe studied by Callahan and Sashin. Here, we present a computational study of the nongradient double cusp, in which the degeneracy of Kadyrov's model is unfolded in codimension eight. Also, we develop a discrete-time cusp model, study the corresponding double cusp, establish its equivalence to the continuous-time double cusp, and discuss some potential applications. We find bifurcations for multiple critical point attractors, periodic attractors, and (for the discrete case) bifurcations to quasiperiodic and chaotic attractors.
[PDF] 14 pages, 44.3 MB

Last revised 21 February 2009 by Ralph