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Coloured-noise-induced transitions in nonlinear structures

Mankin R., Laas T., Soika E., Sauga A., Rekker A., Ainsaar A., Ugaste U.

Nukleonika

2008

Vol. 53, No. 3

127-134

In a stochastic framework, macroscopic approaches are sought to describe microscopic interaction between different species. Coloured-noise-induced transitions in stochastic N-species Lotka-Volterra systems are considered analytically as an appropriate model extendable to many natural and nano-technological processes. All the results discussed are computed by means of a dynamical mean-field approximation. It is demonstrated that interplay of coloured noise and interaction intensities of species can generate a variety of cooperation effects, such as discontinuous transitions of the mean population density, noise-induced Hopf bifurcations and relaxation oscillation. The necessary conditions for the cooperation effects are also discussed. Particularly, it is established that, in the case of the Beddington functional response, in certain parameter regions of the model an increase in noise correlation time can cause multiple transitions (more than two) between relaxation oscillatory regimes and equilibrium states.

Colored-noise-induced anomalous transport in periodic structures

Laas T., Sauga A., Mankin R., Ainsaar A., Ugaste U., Rekker A.

Nukleonika

2006

Vol. 51, nr 1

63-69

Colored-noise-induced anomalous transport phenomena of overdamped particles in a tilted periodic sawtooth potential driven by a nonequilibrium three-level noise and an additive thermal noise are considered analytically. All the physical results discussed are computed by means of exact formulas. It is demonstrated that the particles exhibit anomalous transport properties, such as, multiple change in the sign of the particle flow, absolute negative mobility, negative differential mobility, hypersensitive transport, and hypersensitive differential response. The necessary conditions for various anomalous transport properties are found. It is established that in certain parameter regions an increase in noise parameters (noise-flatness, correlation time, temperature) can facilitate the conversion of noise energy into mechanical work - i.e., the dependence of the efficiency of energy transformation on noise parameters exhibits a bellshaped (resonance) form. Some possible applications to fluctuation-induced separation of particles as well as to the amplification of small signals are also discussed. Our results provide some new perspectives to support elaboration of a model of interaction between plasma beams and construction materials in plasma focus devices.