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)