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Bifurcations and chaos in a predator-prey model with delay and a laser-diode system with self-sustained pulsations. (English) Zbl 1033.37048
Summary: Hopf bifurcations in two models, a predator-prey model with delay terms modeled by “weak generic kernel $aexp\left(-at\right)$” 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.
##### MSC:
 37N25 Dynamical systems in biology 37N20 Dynamical systems in other branches of physics 37G15 Bifurcations of limit cycles and periodic orbits 37D45 Strange attractors, chaotic dynamics 34K18 Bifurcation theory of functional differential equations 78A60 Lasers, masers, optical bistability, nonlinear optics 92D25 Population dynamics (general)