|
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
|