удвоение периода

STOCHASTIC SENSITIVITY OF LIMIT CYCLES FOR «PREDATOR – TWO PREYS» MODEL

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.

PERIOD DOUBLING BIFURCATIONS AND NOISE EXCITATION EFFECTS IN A MULTISTABLE SELF-SUSTAINED OSCILLATORY MEDIUM

The model of a self-oscillatory medium composed from the elements with complex self-oscillatory behavior is studied. Under periodic boundary conditions the stable self-oscillatory regimes in the form of traveling waves with different phase shifts are coexisted in medium. The study of mechanisms of the oscillations period doubling in time is performed for different coexisted modes. For all observed spatially-non-uniform regimes (traveling waves) the period doubling occurs through the appearance of time-quasiperiodic oscillations and their further evolution.