An overdamped Brownian motion in "quartic" potential subjected to periodic driving has been considered. This system for the case of a weak periodic driving has been intensively studied during past decade within the context of stochastic resonance. It has been demonstrated that for the case of predominantly suprathreshold driving (the driving amplitude is significantly larger than the static thr...

The finest state-space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation, the stochastic neighborhoods of deterministic periodic orbits can be computed from distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulas for widths of these distributions in ...

We show that chaotic states situated in the proximity of periodic windows in bifurcation diagrams are eligible for the observation of coherence resonance. In particular, additive Gaussian noise of appropriate intensity can enhance the temporal order in such chaotic states in a resonant manner. Results obtained for the logistic map and the Lorenz equations suggest that the presented mechanism of...

Nonlinear compression of periodic signals is a key feature of the active amplifier in inner ear organs of all vertebrates. Different exponents alpha(0) in [-0.88,-0.5] of the sensitivity vs forcing amplitude |chi| approximately f(alpha(0)) have been observed. Here we calculate analytically the local exponent for a generic oscillator, the normal form of a Hopf bifurcation driven by noise and a p...

The response of strongly nonlinear dynamic systems to stochastic excitation exhibits many interesting characteristics. In this paper, excitation forms like white noise and Gaussian band limited noise are applied to a bilinear system. The nonlinear characteristics cannot be represented sufficiently accurate using statistical linearization techniques. Integration techniques have to be used. The e...

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt (threshold of deterministic running solutions) a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In co...

The wave function of a non-relativistic particle in a periodic potential admits oscillatory solutions, the Bloch waves. In the presence of a random noise contribution to the potential the wave function is localized. We outline a new proof of this Anderson localization phenomenon in one spatial dimension, extending the classical result to the case of a periodic background potential. The proof ma...

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting o...

The detected signal-to-noise power ratio is evaluated for fiber links with periodic amplification. It is shown that the highest ratio is achieved in the limit of a distributed amplifier (g = alpha), but that, alternatively, periodic amplification at intervals of alpha(-1) entails a penalty of less than 2 dB compared with the (ideal) distributed case.

Abstract The periodic transcription output is ubiquitously observed in an isogenic cell population. To understand mechanisms of cyclic behavior transcription, we extend the gene activation process two-state model by assuming that synthesis rate periodic. We derive analytical forms mean transcript level and noise. limits them indicate noise display behaviors. Numerical examples strongly suggest ...