Todd B. Smith, University of Central Florida
Generalized Hopf Bifurcations in a Predator-Prey and a Laser Diode System
Abstract: Generalized Hopf bifurcations in a laser diode system and in a
predator-prey model with delay
terms are considered. The periodic orbit immediately following the
generalized Hopf bifurcation is
constructed using the method of multiple scales, and its stability is analyzed.
For a variety of parameter sets, numerical solutions reveal the existence of stable periodic attractors
and attractors at infinity. Unlike the dynamics following a regular Hopf bifurcation, no quasi-periodic or chaotic behavior was found. This is actually desirable in these physical models, with the periodic regimes
representing either oscillatory populations or oscillator mode operation
in the two systems.
Advisor: S. Roy Choudhury (University of Central Florida)
Collaborators: J. Alvin Bobo III and Craig I. White (University of Central Florida)