Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Fluctuations of Single-Mode Laser Driven by Two Different Kinds of Colored Noise

A single-mode laser with coupling between additive and multiplicative noise terms is investigated when the multiplicative noise and the coupling between two noise terms are colored fluctuations with finite correlation times T1 and τ2. Combining the unified colored noise approximation (UCNA) and the functional analysis, the stationary probability distribution (SPD) and the variance of the laser intensity is derived. It is found that the colored nature of multiplicative noise and the coupling strength between two noise terms can affect both the structure and the height of the SPD, while the colored nature of the coupling between two noise terms can only affect the height of the SPD. The multiplicative noise can enhance the intensity fluctuations while the additive noise can reduce the fluctuations in a laser system. Numerical simulations are presented and consistent to the analytical results.     

First-Order-Like Phase Transition Induced by Two Different Kinds of Noise in Dispersive Optical Bistability

With unified colored noise approximation, the steady state distribution function in dispersive opticalbistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phasetransition is also derived with numerical method. It is found that the number of extremes at non-zero values of theoutput field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-like phase transition.     

First-Order-Like Phase Transition Induced by Two Different Kinds of Noise in Dispersive Optical Bistability

With unified colored noise approximation, the steady state distribution function in dispersive optical bistability including both intensity and phase fluctuations is obtained. The parameter plane of the first-order-like phase transition is a/so derived with numerical method. It is found that the number of extremes at non-zero values of the output field in the steady state distribution function is changed from zero, two to four. It is shown that the strengths of the intensity fluctuation and the phase fluctuation have great effect on the first-order-fike phase transition.     

激光场中两维色噪声的近似计算

从色散型介质中三次激光模型出发，通过泛函导数，应用小于τ近拟计算两维色噪声，得到激光场定态强度分布，研究了定态强度分布的极值点随抽运参量和强度噪声相关时间的变化情况。应用平移1／N展开方法，得到激光场瞬态解，即本征值随抽运参量的变化情况。研究结果表明，抽运参量和噪声相关时间是激光系统出现一级相变类比的关键因素，相位噪声相关时间对强度谱分布中的线宽影响较大。     

Mode competition Effects of a Two Mode Laser with Multiplicative Colored Noise

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First-Order-Like Transition for Dispersive Optical Bistability

The first-order-like phase transition (FOLT) in the dispersive optical bistability is investigated when the fluctuation in the incident light field is considered as colored noise. A unified colored-noise approximation is applied to obtain the steady state distribution (SSD) when either the intensity or phase fluctuations of the incident field are included in the system. For intensity fluctuations only, the curve of SSD is changed from single extreme to two extremes, and then to three extremes. The colored nature of the noise can reduce the fluctuation in the system. However, for phase fluctuations only, the FOLT is mainly induced by the colored nature of the noise. The curve of SSD is changed from single extreme to three extremes directly. There is no FOLT existing for white noise.     

加性噪声对激光一级相变类比的影响

从单模激光场的增益－噪声模型出发,导出了激光场定态强度分布函数,研究了定态分布函数的极值点随加性噪声、乘性噪声和注入信号的变化情况。结果表明,乘性噪声是使激光系统出现一级相变类比的关键因素,注入信号使相变行为减弱,而加性噪声却使得定态分布中极值点的数量和位置出现来回跳跃式变化。     

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.     

Noise induced intercellular propagation of calcium waves

In this paper, we investigate the spatiotemporal dynamics of a bidirectional coupled chain of cells, in which a cell is subjected to an external noise. Noisy oscillations of calcium (Ca²⁺), that is, a bursting-like phenomenon induced by noise with fluctuations in the baseline values of calcium, are induced in the first cell and propagated along the chain with noise suppression. This phenomenon of noise suppression is further investigated by computing the normalized fluctuation of pulse durations. It is therefore found that the noise induced coherence resonance phenomenon occurs at the cellular level. Coherence biresonance behaviour appears in the transmission of noise induced oscillations at appropriate noise intensity or noise coupling (for low noise intensity) and the information flow in each cell can be simultaneously optimized at the optimal value of noise or coupling.     

Phase transitions in a bistable system driven by two colored noises

The colored noise problem is studied from the point of view of consistent Markovian approximations through extending unified colored-noise approximation to the case of two-colored-noise driving systems. A bistable system simultaneously driven by multiplicative and additive colored noise is investigated by means of the extended unified colored-noise approximation. It is found that, for weak strength and color of the additive noise, the form of the stationary probability distribution changes from a unimodal to a bimodal structure via a three modal one as the correlation time of the multiplicative colored noise increases, showing the system undergoes a first order phase transition from a monostable to a bistable state. Numerical simulations support our results. Received 10 August 1998 and Received in final form 23 April 1999     

Entanglement Dynamics and Symmetry Breaking in Symmetric four Qubits GHZ- and W-type States Coupled to Classical Random Telegraph Noise in Mixed Environments

A system of three non-interacting qubits is used as a quantum probe to classify three classical non-Gaussian noises namely, the static noise (SN), colored noise (pink and brown spectrum) and random telegraph noise (RTN), according to their detrimental effects on the evolution of entanglement of the latter. The probe system is initially prepared in the GHZ state and coupled to the noises in independent environments. Seven configurations for the qubit-noise coupling (QNC) are considered. To estimate the destructive influence of each kind of noise, the tripartite negativity is employed to compare the evolution of entanglement in these QNC configurations to each other with the same noise parameters. It is shown that the evolution of entanglement is drastically impacted by the QNC configuration considered as well as the properties of the environmental noises and that the SN is more detrimental to the survival of entanglement than the RTN and colored noise, regardless of the Markov or non-Markov character of the RTN and the spectrum of the colored noise. On the other hand, it is shown that pink noise is more fatal to the system than the RTN and that the situation is totally reversed in the case of brown noise. Finally, it is demonstrated that these noises, in descending order of destructive influence, can be classified as follows: SN > pink noise > RTN > brown noise.

     

Entropic Stochastic Resonance Driven by Colored Noise

The phenomenon of entropic stochastic resonance （ESR） in a two-dimensional confined system driven by a transverse periodic force is investigated when the colored fluctuation is included in the system. Applying the method of unified colored noise approximation, the approximate Fokker-Planck equation can be derived in the absence of the periodic force. Through the escaping rate of the Brownian particle from one well to the other, the power spectral amplification can be obtained. It is found that increasing the values of the noise correlation time and the signal frequency can suppress the ESR of the system.     

Effects of Colored Noise on Periodic Orbits in a One-Dimensional Map

Noise can induce inverse period-doubling transition and chaos. The effects of the colored noise on periodic orbits, of the different periodic sequences in the logistic map, are investigated. It is found that the dynamical behaviors of the orbits, induced by an exponentially correlated colored noise, are different in the mergence of transition, and the effects of the noise intensity ontheir dynamical behaviors are different from the effects of the correlation time of noise. Remarkably, the noise can induce new periodic orbits, namely, two new orbits emerge in the period-four sequence at the bifurcation parameter value μ=3.5, four new orbits in the period-eight sequence at μ=3.55, and three new orbits in the period-six sequence at μ= 3.846, respectively.Moreover, the dynamical behaviors of the new orbits clearly show theresonance like response to the colored noise.     

色噪声对光学双稳态的影响

采用统一色噪声近似构建了由乘法色噪声驱动的纯吸收型光学双稳态状态方程,并分析了色噪声对光学双稳态的影响,将结果与白噪声驱动的光学双稳态进行比较.结果表明:当乘法噪声与加法噪声处在正关联时,增加乘法色噪声的自关联时间r,光学双稳性的区域显著变宽,即磁滞回线面积变大;当乘法噪声与加法噪声处在负关联时,只有乘法噪声较小时,改变乘法色噪声的自关联时间r,光学双稳态才发生改变;当乘法噪声的自相关时间等于零时,本文模型退化为乘法白噪声驱动的光学双稳性状态方程.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance （SR） in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio （SNR） is calculated according to the generalized two-state theory （shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 （1999） 136]）. We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR.     

Noise color and asymmetry in stochastic resonance with silicon nanomechanical resonators

Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and Ornstein-Uhlenbeck noise types. Power spectral densities and residence time distributions provide insight into asymmetry of the bistable amplitude states, and the data sets suggest that 1/f^α noise spectra with increasing noise color (i.e. α) may lead to increasing asymmetry in the system, reducing the achievable amplification. Furthermore, we explore the effects of correlation time τ on stochastic resonance with the use of exponentially correlated noise. We find monotonic suppression of the spectral amplification as the correlation time increases.