This article re-analyses a prey–predator model with a refuge introduced by one of the
founders of population ecology Gause and his co-workers to explain discrepancies between
their observations and predictions of the Lotka–Volterra prey–predator model. They
replaced the linear functional response used by Lotka and Volterra by a saturating functional
response with a discontinuity at a critical prey density. At concentrations below this critical
density prey were effectively in a refuge while at a higher densities they were available to …

In the 30s of the last century Russian biologist Georgii Frantsevich Gause ventured various
experiments to test the biological models of Lotka and Volterra. He found that the actual
interactions of predators and prey contradicted the results found by Lotka and Volterra. In his
experiments there was a distinct chance for the prey and for the predators to die out. In
another setup, with different kinds of predators and prey, there were strong signs that
suggested that there was something like a convergence to a limit cycle. These are results …