stochastic sensitivity.

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.

The response problem of equilibrium and cycles for stochastically forced Verhulst population model is considered. Theoretical and empirical approaches are used for stochastically sensitivity analysis. The theoretical approach is based on the firth approximation method and the empirical approach is based on direct numerical simulation. The correspondence between the two approaches for Verhulst population model is demonstrated. The increase of discrete system sensitivity to external noise in the period­doubling bifurcation zone under transition to chaos is shown.

We consider the population dynamics model «predator – two preys». A deterministic stability of limit cycles of this three­dimensional model in a period doubling bifurcations zone at the transition from an order to chaos is investigated. Stochastic sensitivity of cycles for additive and parametrical random disturbances is analyzed with the help of stochastic sensitivity function technique. Thin effects of stochastic influences are demonstrated. Growth of stochastic sensitivity of cycles for period doubling under transition from order to chaos is shown.