Bifurcations and chaos in a predator–prey model with delay and a laser-diode system with self-sustained pulsations

Hopf bifurcations in two models, a predator–prey model with delay terms modeled by “weak generic kernel aexp(−at)” and a laser diode system, are considered. The periodic orbit immediately following the Hopf bifurcation is constructed for each system using the method of multiple scales, and its stability is analyzed. Numerical solutions reveal the existence of stable periodic attractors, attractors at infinity, as well as bounded chaotic dynamics in various cases. The dynamics exhibited by the two systems is contrasted and explained on the basis of the bifurcations occurring in each.