Dichotomous Noise Research Articles

Dynamics of meandering spiral waves under the modulation of a dichotomous noise

In this paper, we study the effect of a dichotomous noise on meandering spiral dynamics, and exhibit how the cycloid motion of the meandering spiral tip is destroyed by the noise. Switching on the noise does not alter the primary frequency f1 and the secondary frequency f2 in the tip motion, which is different from the case for a periodic dichotomous modulation, where f2 is changed according to two specific rules. However, the dichotomous noise leads to a decrease of the amplitudes at f1 and f2, and the rate of decrease of the amplitude at f2 is larger than that at f2 in the process of increasing the noise intensity or the correlation. The areas with small v-values (SV) are defined, and the distribution and size of the SV areas are analyzed, in order to explain and describe these results. It is also proved that spiral waves can be eliminated by the dichotomous noise with a large amplitude or correlation.

Stochastic Resonance for a SQUID with Dichotomous Resistance

We investigate the response to the ac current for a superconducting quantum interference device (SQUID) with a dichotomous resistance. It is shown that, for some suitably selected parameters' values, stochastic resonance appears for the amplitude of the stationary average voltage of the SQUID versus the correlation time of the dichotomous noise. Our result can provide some useful insights for the investigation of the response of the SQUID (especially for the ones with the nano junctions) to the temporal-periodic signal (including the input ac current, the irradiation microwave, the detected temporal-periodic signal, and the added ac voltage).

Damping Coefficient Induces Stochastic Multiresonance in Bistable System with Asymmetric Dichotomous Noise

Stochastic resonance (SR) and stochastic multiresonance (SMR) phenomena as a function of the underdamping and overdamping coefficients in bistable system with asymmetric dichotomous noise are investigated numerically. By the efficient numerical simulation of the asymmetric dichotomous noise and the fourth-order Runge-Kutta algorithm, we calculate the system responses, the averaged power spectrum, and the signal-noise-ratio (SNR) that can be a measure of the existence of SR and SMR phenomenon. And the effects of damping coefficients on the three characteristics are analyzed. Firstly, it is found that the periodic asymmetric distribution of the particle’s hopping between two potential wells in the system response is gradually weakened as underdamping coefficient is increased to overdamping coefficient. And it also displays the periodic asymmetric distribution under the circumstance of overdamping coefficient. Then the averaged power spectrum exhibits multiple sharp peaks, and the highest peak increases and decreases for underdamping coefficient which is added to overdamping coefficient. Finally, SNR versus the damping coefficient for the system parameters and the noise parameters are acquired and they show multiple peaks and valleys, which illustrates the obvious SMR phenomena in bistable system with asymmetric dichotomous noise.

Noise-Induced Transitions in a Population Growth Model Based on Size-Dependent Carrying Capacity

The stochastic dynamics of a population growth model with size-dependent carrying capacity is considered. The effect of a fluctuating environment on population growth is modeled as a multiplicative dichotomous noise. At intermediate values of population size the deterministic counterpart of the model behaves similarly to the Von Foerster model for human population, but at small and very large values of population size substantial differences occur. In the stochastic case, an exact analytical solution for the stationary probability distribution is found. It is established that variation of noise correlation time can cause noise-induced transitions between three different states of the system characterized by qualitatively different behaviors of the probability distributions of the population size. Also, it is shown that, in some regions of the system parameters, variation of the amplitude of environmental fluctuations can induce single unidirectional abrupt transitions of the mean population size.

Stochastic resonance in the overdamped fractional oscillator subject to multiplicative dichotomous noise

With the increasingly deep studies in physics and technology, the behavior of fractional oscillators have become the focus of scientific research. In this paper, the stochastic resonance (SR) mechanism of the overdamped fractional oscillator subject to multiplicative dichotomous noise is extensively investigated. Using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression for complex susceptibility is obtained. Resorting to numerical simulations, the SR phenomenon of the overdamped fractional oscillator is studied. Especially, the frequency of the external periodic force that induces multiresonance.

Enhancement of electron spin lifetime in GaAs crystals: The benefits of dichotomous noise

The electron spin relaxation process in n-type GaAs crystals driven by a fluctuating electric field is investigated. Two different sources of fluctuations are considered: (i) a symmetric dichotomous noise and (ii) a Gaussian correlated noise. Monte Carlo numerical simulations show, in both cases, an enhancement of the spin relaxation time by increasing the amplitude of the external noise. Moreover, we find that the electron spin lifetime vs. the noise correlation time: (i) increases up to a plateau in the case of dichotomous random fluctuations, and (ii) shows a nonmonotonic behaviour with a maximum in the case of bulks subjected to a Gaussian correlated noise.

Stochastic oscillator with random mass: New type of Brownian motion

The model of a stochastic oscillator subject to additive random force, which includes the Brownian motion, is widely used for analysis of different phenomena in physics, chemistry, biology, economics and social science. As a rule, by the appropriate choice of units one assumes that the particle’s mass is equal to unity. However, for the case of an additional multiplicative random force, the situation is more complicated. As we show in this review article, for the cases of random frequency or random damping, the mass cannot be excluded from the equations of motion, and, for example, besides the restriction of the size of Brownian particle, some restrictions exist also of its mass. In addition to these two types of multiplicative forces, we consider the random mass, which describes, among others, the Brownian motion with adhesion. The fluctuations of mass are modeled as a dichotomous noise, and the first two moments of coordinates show non-monotonic dependence on the parameters of oscillator and noise. In the presence of an additional periodic force an oscillator with random mass is characterized by the stochastic resonance phenomenon, when the appearance of noise increases the input signal.

Control of logic gates by dichotomous noise in energetic and entropic systems

We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a "logical" resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.

Effect of two asymmetries on current of a Brownian particle

A Brownian particle in an asymmetric periodic potential and subjected to an asymmetric dichotomous noise was investigated. In the frame of Fokker-Planck equation, exact expression of current of the system was derived. By means of numerical calculations, the results indicate that: (i) as the symmetry of either potential or noise is broken, a steady current will form; (ii) as the two symmetries are broken simultaneously, the current does not always appear, dependent on values of symmetric parameters of the potential and the noise; (iii) the current exhibits non-monotonic behavior as a function of symmetric parameter of the potential, while monotonic behavior as a function of symmetric parameter of the noise; (iv) in the case the potential symmetry is not broken seriously, the current is greatly influenced on by the noise symmetric parameter; (v) absolute values of the current as a function of height of potential barrier first increase then approach to saturation as the spatial potential is symmetric, while varies monotonically as the dichotomous noise is symmetric. In addition, the planes of the two symmetric parameters, which determine directions of the current, are drawn.

Optimal control of a class of piecewise deterministic processes

A new control strategy for a class of piecewise deterministic processes (PDP) is presented. In this class, PDP stochastic processes consist of ordinary differential equations that are subject to random switches corresponding to a discrete Markov process. The proposed strategy aims at controlling the probability density function (PDF) of the PDP. The optimal control formulation is based on the hyperbolic Fokker–Planck system that governs the time evolution of the PDF of the PDP and on tracking objectives of terminal configuration with a target PDF. The corresponding optimization problems are formulated as a sequence of open-loop hyperbolic optimality systems following a model predictive control framework. These systems are discretized by first-order schemes that guarantee positivity and conservativeness of the numerical PDF solution. The effectiveness of the proposed computational control framework is validated considering PDP with dichotomic noise.

The Availability of Logical Operation Induced by Dichotomous Noise for a Nonlinear Bistable System

Instead of a continuous system driven by Gaussian white noise, logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise, which shows a phenomenon different from Gaussian white noise. We can realize two parallel logical operations by simply adjusting the values of these two thresholds. Besides, to quantify the reliability of obtaining the correct logic output, we numerically calculate the success probability, and effects of dichotomous noise on the success probability are observed, these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise.

Analytical results for integrate-and-fire neurons driven by dichotomous noise

Models of the integrate-and-fire type have been widely used in the study of neural systems [1]. Usually, they consist of an evolution equation for the neuron's membrane voltage, complemented by a fire-and-reset rule that is applied once a voltage threshold is crossed. This minimalist description has allowed impressive analytical insights, for instance into neuronal information transmission properties [2], the effect of input correlations [3], or the dynamics of whole networks [4]. Further, it can be readily extended to include more complex behavior, such as spike-frequency-adaptation [5], which can then be studied in a well-understood setting. The synaptic input to the neuron is usually modeled as a sequence of spikes with stochastic arrival times; mathematically speaking, it is a Poisson process where each event is a delta spike (shot noise). As such discrete input is notoriously difficult to treat analytically (but see [6]), many studies have employed the so called diffusion approximation, modeling the massive synaptic bombardment as Gaussian white noise. Here, we consider a general integrate-and-fire neuron that is driven by dichotomous noise, i.e. input that switches stochastically between two levels (cf. Figure ​Figure1A,1A, see [7] for a similar setup). Input of this kind is of interest because it is temporally correlated, in contrast to the white noise often used. Also, when switching rates are asymmetric, it converges to excitatory shot noise in the limit of small correlation time. Further, it can model the switching between up and down-states of presynaptic network activity, or bursting activity of a presynaptic neuron. Figure 1 A) Sample time course of a two state noise. B) Corresponding voltage dynamics of a leaky integrate-and-fire neuron. C) Stationary distribution of this neurons membrane voltage. Units are arbitrary. We derive analytical expressions for firing-rate, CV and the steady-state voltage distribution of this system and verify them by numerical simulation. Furthermore, we study the transmission of a weak signal through such a neuron.

Dichotomous-noise-induced pattern formation in a reaction-diffusion system

We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.

Focusing in multiwell potentials: Applications to ion channels

We investigate nonequilibrium stationary distributions induced by stochastic dichotomous noise in double-well and multiwell models of ion channel gating kinetics. The channel kinetics is analyzed using both overdamped Langevin equations and master equations. With the Langevin equation approach we show a nontrivial focusing effect due to the external stochastic noise, namely, the concentration of the probability distribution in one of the two wells of a double-well system or in one or more of the wells of the multiwell model. In the multiwell system, focusing in the outer wells is shown to be achievable under physiological conditions, while focusing in the central wells has proved possible so far only at very low temperatures. We also discuss the strength of the focusing effect and obtain the conditions necessary for maximal focusing to appear. These conditions cannot be predicted by a simple master equation approach.

Mapping absorption processes onto a Markov chain, conserving the mean first passage time

The dynamics of a multidimensional system is projected onto a discrete state master equation using the transition rates W(k → k′; t, t + dt) between a set of states {k} represented by the regions {ζk} in phase or discrete state space. Depending on the dynamics Γi(t) of the original process and the choice of ζk, the discretized process can be Markovian or non-Markovian. For absorption processes, it is shown that irrespective of these properties of the projection, a master equation with time-independent transition rates can be obtained, which conserves the total occupation time of the partitions of the phase or discrete state space of the original process. An expression for the transition probabilities is derived based on either time-discrete measurements {ti} with variable time stepping Δ(i + 1)i = ti + 1 − ti or the theoretical knowledge at continuous times t. This allows computational methods of absorbing Markov chains to be used to obtain the mean first passage time (MFPT) of the system. To illustrate this approach, the procedure is applied to obtain the MFPT for the overdamped Brownian motion of particles subject to a system with dichotomous noise and the escape from an entropic barrier. The high accuracy of the simulation results confirms with the theory.

Mass dependence of instabilities of an oscillator with multiplicative and additive noise

We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focusing on the dependence of the instability threshold on the mass. For multiplicative noise in the damping, the energy instability threshold is crossed as the mass is decreased, as long as the smaller damping is in fact negative. For multiplicative noise in the stiffness, the situation is more complicated and in fact the energy transition is reentrant for intermediate noise strength and damping. For multiplicative noise in the mass, the results depend on the implementation of the noise. One can take the velocity or the momentum to be conserved as the mass is changed. In these cases increasing the mass destabilizes the system. Alternatively, if the change in mass is caused by the accretion and loss of particles to the Brownian particle, these processes are asymmetric with momentum conserved upon accretion and velocity upon loss. In this case, there is no instability, as opposed to the other two implementations. We also present the mass dependence of the instability threshold for the first moment. Finally, we study the distribution of the energy, finding a power-law cutoff at a value that increases with time.

Исследование условий стационарности моментов случайного процесса, имеющего в своей структуре мультипликативный дихотомический шум с функцией распределения Эрланга первого порядка и параметры, связанные пропорцией золотого сечения

Исследование условий стационарности моментов случайного процесса, имеющего в своей структуре мультипликативный дихотомический шум с функцией распределения Эрланга первого порядка и параметры, связанные пропорцией золотого сечения

The resonant behavior of a linear harmonic oscillator with fluctuating mass

The mass of Brownian particle is fluctuant in a viscous medium, because the molecules of surrounding medium may randomly stick on it. This mass fluctuation influence on the system resonant behavior is studied by modeling it as a symmetric dichotomous noise. Using Shapiro-Loginov formula and Laplace transformation, the analytical expression of system steady response amplitude is presented. The corresponding numerical results are used to discuss system resonant behavior. Furthermore, the reliability of theoretical results is tested by simulation experiments. All the research results show that: 1) the system steady response is a simple harmonic vibration which has the same frequency as the driving signal; 2) with the variations of driving frequency, oscillator mass and noise parameters, the system presents real resonance, parameter induced resonance and stochastic resonance phenomenon, respectively; 3) because of the mass fluctuation, some new resonant forms are observed, such as one-peak and one-valley resonance, two-peak resonance, etc.

Stochastic Resonance in a Linear Fractional Langevin Equation

The fractional Langevin equation is derived from the generalized Langevin equation driven by the additive fractional Gaussian noise. We investigate the stochastic resonance (SR) phenomenon in the underdamped linear fractional Langevin equation under the external periodic force and multiplicative symmetric dichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expressions of the amplitude and signal-to-noise ratio (SNR) of the system. By studying the impacts of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude and SNR. The results indicate that the bona fide SR, conventional SR and the wide sense of SR phenomena occur in the proposed linear fractional system.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance (ESR) in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio (SNR) is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.