Trichotomous Noise Research Articles

Stochastic resonance in coupled underdamped bistable systems driven by symmetric trichotomous noises

In this work, we analyze the phenomenon of stochastic resonance (SR) in coupled underdamped bistable systems induced by independent symmetric trichotomous noises. Firstly, the system is found to exhibit intermittent jumping motion between two wells in an optimal range of noise values. Then, the effects of noise on the output power spectrum of the system are characterized. It demonstrates that stochastic resonance behavior can occur above a particular value of noise strength. Finally, the signal-noise-ratio (SNR) for different parameters is computed numerically. Remarkably, for different parameters, a non-monotonic behavior of SNR is shown and the impacts of trichotomous noise and Gaussian white noise on the SNR curve are researched.

Trichotomous noise controlled signal amplification in a generalized Verhulst model

The long-time limit of the probability distribution and statistical moments for a population size are studied by means of a stochastic growth model with generalized Verhulst self-regulation. The effect of variable environment on the carrying capacity of a population is modeled by a multiplicative three-level Markovian noise and by a time periodic deterministic component. Exact expressions for the moments of the population size have been calculated. It is shown that an interplay of a small periodic forcing and colored noise can cause large oscillations of the mean population size. The conditions for the appearance of such a phenomenon are found and illustrated by graphs. Implications of the results on models of symbiotic metapopulations are also discussed. Particularly, it is demonstrated that the effect of noise-generated amplification of an input signal gets more pronounced as the intensity of symbiotic interaction increases.

Stochastic resonance in a linear system with random damping parameter driven by trichotomous noise

The stochastic resonance (SR) in a second-order linear system driven by a trichotomous noise and an external periodic signal is investigated. By the use of the properties of the trichotomous noise and the Shapiro–Loginov formula, the exact expression for the output spectral amplification (SPA) of the system is obtained. The non-monotonic influence of the coefficient of the trichotomous noise on the SPA is found. It is shown that the SPA is a non-monotonic function of the amplitude, the correlation rate and the probability of the trichotomous noise. The SPA varies non-monotonically with the frequency of the driving signal, the damping coefficient and the frequency of the linear system.

Stochastic resonance in a harmonic oscillator with damping trichotomous noise

In this paper, the phenomenon of stochastic resonance (SR) in a prototype fluctuating damping harmonic oscillator with trichotomous Markovian noise is investigated. The exact expression of output amplitude gain has been calculated using the well-known Shapiro–Loginov formula. The phenomenon of SR has been found in a broad sense—that is, the non-monotonic behavior of output amplitude gain as a function of noise parameters. Then the influences of noise amplitude, noise switching rate, and noise flatness on the output amplitude gain have also been discussed. Finally, the reverse resonance phenomenon has been presented.

Oscillator with random trichotomous mass

In addition to the case usually considered of a stochastic harmonic oscillator subject to an external random force (Brownian motion in a parabolic potential) or to a random frequency and random damping, we consider an oscillator with random mass subject to an external periodic force, where the molecules of a surrounding medium, which collide with a Brownian particle are able to adhere to the oscillator for a random time, changing thereby the oscillator mass. The fluctuations of mass are modelled as trichotomous noise. Using the Shapiro–Loginov procedure for splitting the correlators, we found the first two moments. It turns out that the second moment is a non-monotonic function of the characteristics of noise and periodic signal, and for some values of these parameters, the oscillator becomes unstable.

Trichotomous noise induced stochastic resonance in a linear system

We investigate stochastic resonance in an underdamped linear system subjected to multiplicative trichotomous noise. We carry out the Shapiro–Loginov formula to find the exact expression of output amplitude gain, and the impacts of the input signal frequency and noise parameters will be observed, such as noise switching rate or noise correlation time, noise amplitude and noise flatness. Then one can find the stochastic resonance for the proposed linear system.

Generalized Langevin equation with multiplicative trichotomous noise

The influence of noise flatness and memory-time on the dynamics of a generalized Langevin system driven by an internal Mittag-Leffler noise and by a multiplicative trichotomous noise is studied. In the asymptotic limit at a short memory time the dynamics corresponds to a system with a pure power-law memory kernel for a viscoelastic type friction. However, at long and intermediate memory times the behaviour of the system has a qualitative difference. In particular, a critical memory time and a critical memory exponent have been found, which mark dynamical transitions in the resonant behaviour of the system. The obtained results show that the model considered is quite robust and may be of interest also in cell biology.

Effect of Charge Fluctuations on Conduction in Biological Ion Channels

How open ion channels are able to conduct ions with a throughput comparable to free diffusion, and yet remain highly selective, is an unresolved scientific conundrum of long standing. To shed new light on this problem, the effect of charge fluctuations on the conduction of open ion channels is investigated theoretically. The model considered is a cylindrical channel across the membrane bathed by two solutions of different concentration. The charge fluctuations at the channel mouth are analyzed using Brownian Dynamics simulations and shown to have the form of trichotomous noise on the timescale of nanoseconds. The channel potential with a local minimum at the selectivity site due to the fixed wall charge is calculated by solution of the 3D Poisson equation for two configurations, with one ion moving along the channel axis in the presence or absence of the fluctuating charge at the channel mouth. It is shown that narrow channels act as electrostatic amplifiers of the modulation of the potential barriers at the selectivity site, due to charge fluctuations at the channel mouths. This modulation at the selectivity site was largely neglected in earlier research. It results in a leading order contribution to the transition rates of open ion channels. The proposed model of ion permeation takes into account the dynamical effect of the charge fluctuations through the resultant shot noise, which flips the electrostatic potential at the selectivity site, causing it to fluctuate between three values at a rate corresponding to the random arrivals of ions at the channel mouth. The model is applied to calculation of the current-voltage characteristics of Gramicidin A channel for different concentrations and is shown to be in good agreement with experimental results, including the effect of current saturation at high concentrations.

Constructive influence of noise flatness and friction on the resonant behavior of a harmonic oscillator with fluctuating frequency

The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.

Noise-flatness-induced hypersensitive transport in tilted periodic sawtooth potentials

The noise-flatness-induced hypersensitive transport of overdamped Brownian particles in a tilted periodic sawtooth potential driven by a multiplicative nonequilibrium three-level noise and additive white noise is considered. The study is a follow-up of one of our earlier papers on trichotomous-noise-induced hypersensitive transport [Mankin et al., Phys. Rev. E 68 (2003) 011105]. In the current paper the exact formula for the stationary current is presented. All the physical results discussed are computed by means of the exact formula. It is demonstrated that (i) at low temperatures the enhancement of current is hypersensitive to the applied small static tilting force, (ii) the stationary macroscopic current has a bell-shaped dependence on the parameters, correlation time and flatness, of multiplicative noise which occurs even in the case of large (compared to the ultrasmall DC signal) additive thermal noise, and (iii) at low temperatures and small values of the switching rate, the differential mobility as a function of the tilting force has local minima in a finite range of the force. Implications of the case of multiplicative trichotomous noise are compared with the results of a deterministic square-wave stimulus.

Trichotomous noise: applications to stochastic transport

Trichotomous noise: applications to stochastic transport

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. Stability and instability conditions and colored-noise-induced discontinuous transitions (catastrophic shifts) in the model are investigated. In some cases the mean field exhibits hysteresis as a function of the noise parameters. It is shown that the occurrence of catastrophic shifts can be controlled by noise parameters, such as correlation time, amplitude, and flatness. The dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams. Implications of the results on some modifications of the model are discussed.

Constructive role of temperature in ratchets driven by trichotomous noise.

The dynamics of an overdamped Brownian particle in a piecewise linear spatially periodic potential subjected to both thermal and colored symmetric three-level Markovian (trichotomous) noises is investigated. In the case of large flatness, the exact formula for the stationary current is presented. The dependence of the current on the system parameters is analyzed and the conditions for the occurrence of current reversals are found. It is shown that the direction and value of the current can be controlled by a thermal noise. Asymptotic formulas for the current for various limits of the noise parameters are calculated and compared with the results of other authors. For small noise amplitudes, it is demonstrated that the temperature at which the current is maximized is proportional to the height of the potential barrier, being a slowly varying function of the other system parameters.

Current reversals in ratchets driven by trichotomous noise

The colored three-level Markovian noise-driven nonequilibrium dynamics of overdamped Brownian particles in a spatially periodic asymmetric potential (ratchet) is investigated. An explicit second-order linear ordinary differential equation for the stationary probability density distribution is obtained for the process. In the case of a piecewise linear potential with an additive three-level (trichotomous) noise the exact formula for the stationary current is presented. The dependence of the current reversals on the noise parameters is investigated in detail and illustrated by a phase diagram. Asymptotic formulas for the current for various limits of the noise parameters are found and compared with the results of other authors. Applications to the fluctuation-induced separation of particles are also discussed.

Trichotomous noise-induced transitions.

A nonlinear one-dimensional process driven by a multiplicative exponentially correlated three-level Markovian noise (trichotomous noise) is considered. An explicit second-order linear ordinary differential equation for the stationary probability density distribution is obtained for the process. In the case of a linear process with an additive trichotomous noise the exact formula for the steady-state distribution is obtained. The well-known dichotomous noise can be regarded as a special case of the trichotomous noise. As a rule, the system variable has three specific values where the probability density distribution can be singular. For the case of the Hongler model the dependence of the behavior of the stationary probability density on the noise parameters is investigated in detail and illustrated by a phase diagram. Applications to the Gompertz and Verhulst models are also discussed.