равновесия

We consider the population dynamics model «predator–prey». Equilibria and limit cycles of system are studied from both deterministic and stochastic points of view. Probabilistic properties of stochastic trajectories are investigated on the base of stochastic sensitivity function technique. The possibilities of stochastic sensitivity function to analyse details and thin features of stochastic attractors are demonstrated.

We consider the Hopf system as a classical model of a stiff birth of a cycle. In the presence of parametrical and additive random disturbances, various types of the stochastic attractors are observed. The solution of the corresponding Fokker–Planck–Kolmogorov equation is found. The qualitative changes of the form for stochastic attractors under multiplicative noise are shown. The phenomenon of backward stochastic bifurcations is described in details.