Bistability and cycles in the population dynamics of systems with multiplicative noise (Q1374959)

The mathematical biophysics of interacting populations has developed in many directions. However, problems connected with the investigation of parametric noise action of the environment on the dynamics of biological communities are still far from an exhaustive solution. Such problems can be solved precisely only if population dynamics is either reducible to one-dimensional dynamics or satisfies the detail balance condition. However, numerical modeling does not allow one to accurately distinguish the most probable regimes of population dynamics, especially for high noise intensity. We propose a new approximate method for the investigation of many-dimensional population dynamics under a parametric random external action. It is shown that, for a sufficiently high noise intensity, bistability induced by noise and noise damping of the oscillation regime can appear in a predator-prey system.