Search

We investigate coherence resonance of corporate finance in a stochastic predator-prey model for creditors and producers. The stochastic predator-prey model with only considering financial risk and the Integral method of an improvement parameter estimation are proposed. Then the coefficient of variation (CV) of the interspike intervals is used to measure the phenomenon of coherence resonance. The simulating and empirical results indicate that (i) the phenomenon peak death is induced by higher noise strength and system parameters; (ii) the phenomenons of coherence and anti-coherence resonance are observed in the function of CV vs. noise strength; (iii) the critical phenomenon of resonance enhancement and inhibition is induced by some values of system parameters. In addition, a good agreement can be found between theoretical results and real financial data of Chinese companies.

The dynamic characteristic of macromolecule is mainly subject to the fluctuation of rate constant and this phenomenon is usually considered as dynamic disorder (DD). In order to detect the DD nature in the bio-molecule system more accurately, here we propose a theoretical framework based on the two-dimensional (2D) free-energy landscape including the pulling coordinate and other slow conformational variables. The generalized Langevin equation (GLE) with fractional Gaussian noise (fGn) and the power-law memory kernel are used on this landscape for the research. The transition rate, which depends on both intrinsic barrier height and noise strength ratio, has been analyzed under the condition of external force. The particular discrepancies were investigated between the kinetics of the transitions with and without DD. We find that the discrepancies relied on the barrier height and the noise strength ratio. Taken together, our study illustrates the importance of the DD characteristics, which should be taken into account during the research into the single-molecule pulling experiments.

This study aims to provide a theoretical analysis for investigating the consensus behavior of opinion dynamics in noisy environments. We present how random noises significantly help “synchronize” opinions in the Hegselmann–Krause (HK) model. We prove that when noise strength is below the critical value, the opinions of the noisy HK dynamics tend to achieve “consensus” (referred to as quasi-consensus due to noise) in finite time. Fragmentation of HK dynamics tends to eventually vanish when persistent noise is present. Meanwhile, we verify that the opinions almost surely divide infinite times when noise strength exceeds the critical value.

We explore the profiles of self-polarization effect (SPE) of doped G a A s QD under simultaneous presence of hydrostatic pressure (HP), temperature and in presence of noise. Noise term carries Gaussian white character and it has been administered to the system via two different pathways; additive and multiplicative. Profiles of SPE have been monitored as a function of HP, temperature and noise strength. Under a given condition of HP and temperature, noise marks its prominent signature on the SPE profile. However, the extent to which noise affects the SPE profile visibly depends on the noise strength and the pathway through which noise is introduced. As interesting observations we have found that SPE exhibits minimization at a pressure of ∼ 170 kbar in absence of noise and at ∼ 150 kbar when noise is present. Furthermore, in presence of multiplicative noise SPE exhibits a very faint decrease with increase in T up to T ∼ 420 K. However, beyond T ∼ 420 K, further increase in temperature causes abrupt fall of SPE in a highly sharp way. The findings highlight viable ways of tuning SPE of doped QD system through subtle interplay between HP, temperature and noise.

In this paper, the asymptotic behavior of a stochastic Cucker–Smale model with multiplicative excitation is investigated. Firstly, it is proven that stochastic flocking occurs for the communication weight originally proposed by Cucker and Smale if the noise strength is sufficiently small. Then, a non-flocking result under the effect of large noise is provided. In addition, the kinematics of the macroscopic variables is addressed which can be regarded as an effective supplement of consensus dynamics.

We present a new kinetic Cucker–Smale–Fokker–Planck (CS-FP) type equation with a degenerate diffusion, which describes the dynamics for an ensemble of infinitely many Cucker–Smale particles in a random environment. The asymptotic dynamics of the CS-FP equation exhibits a threshold-like phenomenon depending on the relative strength between the coupling strength and the noise strength. In the small coupling regime, the noise effect becomes dominant, which induces the velocity variance to increase to infinity exponentially fast. In contrast, the velocity alignment effect is strong in the large coupling regime, and the velocity variance tends to zero exponentially fast. We present the global existence of classical solutions to the CS-FP equation for a sufficiently smooth initial datum without smallness in its size. For the kinetic CS-FP equation with a metric dependent communication weight, we provide a uniform-in-time mean-field limit from the stochastic CS-model to the kinetic CS-FP equation without convergence rate.

In this paper, we investigate the stochastic resonance phenomenon in a vegetation ecological system with time delay, at which the vegetation dynamics is assumed to be disturbed by both intrinsic and extrinsic noises. The signal-to-noise ratio is calculated when a weak periodic signal is added to the system. The impacts of time delay τ and correlation strength k between two noises on the signal-to-noise ratio are discussed, respectively. Our research results show that: (i) the increase of τ or k can enhance the stochastic resonance in the signal-to-noise ratio as a function of intrinsic noise strength α ; (ii) on the contrary, the increase of τ or k can weaken the stochastic resonance in the signal-to-noise ratio as a function of extrinsic noise strength D ; and (iii) the increase of τ can lead to double stochastic resonance phenomenon in the signal-to-noise ratio as a function of k .

The auto-correlation function and the cross-correlation function of an autonomous stochastic system with time delays are investigated. We obtain the distribution curves of the auto-correlation function C x ( s ) and C y ( s ) , and the cross-correlation function C x y ( s ) and C y x ( s ) of the stochastic dynamic variables by the stochastic simulation method. The delay time changes prominently the behaviors of the dynamical variables of an autonomous stochastic system, which makes the auto-correlation and the cross-correlation of the autonomous stochastic system alternate oscillate periodically from positive to negative, or from negative to positive, decrease gradually, and finally tends to zero with the decay time. The delay time and the noise strength have important impacts for the auto-correlation and the cross-correlation of the autonomous stochastic delay system. The delay time enhances the auto-correlation and the cross-correlation, on the contrary, the noise strength lowers the auto-correlation and the cross-correlation. Under the time delay, by comparison we further show differences of the auto-correlation and the cross-correlation between the dynamical variables x and y .

Bistable switches are frequently encountered in biological systems. Typically, a bistable switch models a binary decision where each decision corresponds to one of the two stable equilibria. Recently, we showed that the global decision-making process in bistable switches strongly depends on a particular equilibrium point of these systems, their saddle point. In particular, we showed that a saddle point with a time-scale separation between its attractive and repulsive directions can delay the decision-making process. In this paper, we study the effects of white Gaussian noise on this mechanism of delayed decision-making induced by the saddle point. Results show that the mean decision-time strongly depends on the balance between the initial distance to the separatrix and the noise strength.

We study how long pause-prone sites, commonly sequence-dependent, affect transcription and RNA temporal levels in a delayed stochastic model of transcription at the single nucleotide level. We vary pause propensity, duration and the probability of premature termination of elongation at the pause site. We also study the effects of multiple pause sites. We show that pause sites can be used to fine-tune noise strength and burst size distribution of RNA levels. Varying pause rate and duration alone affects bursting but noise is not significantly affected. Noise strength can be changed by varying both parameters and, even more pronouncedly, by varying the probability of premature termination. Adding multiple pause sites amplifies the increase in noise and bursting. This regulatory mechanism of noise and bursting, being evolvable, may partially explain how different genes exhibit a wide spectrum of different behaviors. The results might assist the engineering of genes with a desired degree of noise.

The forced and overdamped motion of non-interacting particles in a periodic asymmetric potential is studied. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with non-correlated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength. These non-trivial results are explained on the basis of the synchronized motion of the individual particles in the perfect lattice.

The collective motion of the globally coupled maps driven by the external noise is investigated when the number of the maps is finite. A simplest collective motion for the globally coupled maps is found by controlling the noise strength. The dimension of the collective motion exhibits a minimum as a function of the external noise strength when the collective motion is the simplest.

Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the fractal repeller and the critical point of the map. Two methods give a precise meaning to the asymptotic expansion, Borel summation and Shafer approximants. These can then be compared with the escape rate as computed by alternative methods., Comment: 15 pages, 5 postscript figures incorporated into the text; v2: Quadratic Pade (Shafer) method added, also a few references

Phase turbulence is suppressed by applying common noise additively to the Kuramoto-Sivashinsky type equation, and the noise-induced phase synchronization is realized. The noise strength necessary for the suppression of phase turbulence is evaluated theoretically., 7 pages, 4 figures

The presence of noise in non linear dynamical systems can play a constructive role, increasing the degree of order and coherence or evoking improvements in the performance of the system. An example of this positive influence in a biological system is the impulse transmission in neurons and the synchronization of a neural network. Integrating numerically the Fokker-Planck equation we show a self-induced synchronized oscillation. Such an oscillatory state appears in a neural network coupled with a feedback term, when this system is excited by noise and the noise strength is within a certain range., Comment: 12 pages, 18 figures

The coarsening of domains of striped patterns in the presence of a multiplicative noise is examined through numerical simulations of the cell-dynamical-system model of the Swift–Hohenberg equation. The growth exponent of the characteristic length scale is shown to increase with the noise strength, demonstrating the noise-enhanced domain orientation.

We study the two time correlation for the noise driven dynamics of the double-well oscillator in the Suzuki regime. It is seen that for very small noise strength the correaltion function shows a lack of translational invariance for very long times characterised by the Suzuki scaling variable. We see that in this strongly out-of-equilibrium situation, the conventional mode-coupling approximation is not a convenient tool., Comment: 8 pages, no figure

We investigate the presence of two-particle bound states in the stochastic dynamics generator of weakly coupled Ginzburg–Landau models, and study their dependence on the noise strength. For the space dimension d ⩽3, by analyzing the Bethe–Salpeter equation in the ladder approximation, we show that a bound state appears but disappears again at a higher value of the noise intensity. Furthermore, we show that in the case of the polynomial interaction with a negative quartic term the bound state appears and disappears for the noise intensity much smaller than that for the interaction with the quartic term positive. We also describe the curves giving the bound states masses in terms of the noise strength, which show the effect that, for a suitable noise intensity, the two-particle bound state mass becomes smaller than the one-particle mass.

In this paper we present a hydrodynamic approach to describe the motion of migrating bacteria as a special class of self-propelled systems. Analytical and numerical calculations has been performed to study the behavior of our model in the turbulent-like regime and to show that a phase transition occurs as a function of noise strength. Our results can explain previous experimental observations as well as results of numerical simulations., Comment: 8 pages, 10 figures

We study collective dynamics in a chain of harmonically coupled particles subjected to degenerate but asymmetric on-site double-well potentials and driven by white and exponentially correlated noise. The difference of frequencies of small-amplitude oscillations in the vicinity of the wells appears to be a sufficient condition for the existence of the soliton ratchet effect. We find directed thermally activated soliton motion while at certain critical values of either the correlation time or noise strength, a reversal (switching) of the direction of motion takes place. Furthermore, we observe stochastic soliton transport directed against an applied d.c. field.

The well-known integration method along characteristic curves is improved in two respects: the second order in the noise strength is included, and the essential curves are selected from the beginning. One thus obtains the minimum numerical information which is necessary to compute the transition rates.

Power spectra of discrete dynamical systems at the threshold of chaos contain line series obeying S ω ∞ ω μ for small ω. We explain μ in terms of the Feigenbaum rescaling parameter α. Another parameter β related to the noise strength of states of periodic chaos and recently numerically determined by Huberman and Zisook is related to α as well.