Modeling the dynamics of natural rotifer populations: phase-parametric   analysis
  A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of these parameters were investigated by methods of bifurcation theory. A phase-parametric portrait of the model was constructed and domains of population persistence (stable equilibrium, periodic and a-periodic oscillations of population size) as well as population extinction were identified and investigated. The criteria for population persistence and approaches to determining critical parameter values are described. The results identify parameter values that lead to population extinction under various environmental conditions. They further illustrate that the likelihood of extinction can be substantially increased by small changes in environmental quality, which shifts populations into new dynamical regimes. 
Faina S. Berezovskaya, Georgy P. Karev, and Terry W. Snell