Hopf bifurcation in a structured population model for the sexual phase of monogonont rotifers

We are studying a population of monogonont rotifers in the context of non-linear age-dependent models. In the sexual phase of their reproductive cycle we consider the population structured by age, and composed of three subclasses: virgin mictic females, mated mictic females, and haploid males. The model system has a unique stationary population density which is stable as long as a parameter, related to male-female encounter rate, remains below a critical value. When the parameter increases beyond this critical value, the stationary solution becomes unstable and a stable limit cycle (isolated periodic orbit) appears. The occurrence of this supercritical Hopf bifurcation is shown analytically.