Generalized Hopf bifurcations in a predator-prey model with delay terms modeled by “weak generic kernel are considered. The periodic orbit immediately following the generalized Hopf bifurcation is constructed using the method of multiple scales, and its stability is analyzed. Numerical solutions reveal the existence of attractors at infinity and bounded chaotic dynamics in various cases. The dynamics are explained on the basis of the bifurcations occurring in each. Chaotic regimes are characterized using power spectra, correlation functions, and fractal dimensions.

generalized Hopf bifurcations, predator-prey systems, chaos.