Resonant behavior of a fractional oscillator with fluctuating frequency.

The long-time behavior of the first moment for the output signal of a fractional oscillator with fluctuating frequency subjected to an external periodic force is considered. Colored fluctuations of the oscillator eigenfrequency are modeled as a dichotomous noise. The viscoelastic type friction kernel with memory is assumed as a power-law function of time.

Thermally enhanced stability in fluctuating bistable potentials.

Overdamped motion of Brownian particles in an asymmetric double-well potential driven by an additive nonequilibrium three-level noise and a thermal noise is considered. In the stationary regime, an exact formula for the mean occupancy of the metastable state is derived, and the phenomenon of enhancement of stability versus temperature is investigated. It is established that in a certain region of the system parameters the mean occupancy can be either multiply enhanced or suppressed by variations of temperature.

Colored-noise-induced Hopf bifurcations in predator-prey communities.

A broad class of (N+1) -species ratio-dependent predator-prey stochastic models, which consist of one predator population and N prey populations, is considered. The effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise. In the framework of the mean-field theory, approximate self-consistency equations for prey-populations mean density and for predator-population density are derived (to the first order in the noise variance).

Colored-noise-induced discontinuous transitions in symbiotic ecosystems.

A symbiotic ecosystem is studied by means of the Lotka-Volterra stochastic model, using the generalized Verhulst self-regulation. The effect of fluctuating environment on the carrying capacity of a population is taken into account as dichotomous noise. The study is a follow-up of our investigation of symbiotic ecosystems subjected to three-level (trichotomous) noise [Phys.

Trichotomous-noise-induced catastrophic shifts in symbiotic ecosystems.

An N-species Lotka-Volterra stochastic model of a symbiotic ecological system with the Verhulst self-regulation mechanism is considered. The effect of fluctuating environment on the carrying capacity of a population is modeled as the colored three-level Markovian (trichotomous) noise. In the framework of the mean-field theory an explicit self-consistency equation for stationary states is presented.