Correlation Time Of Multiplicative Noise Research Articles

Impact of Colored Noise on Population Model with Allee Effect**Supported by the National Natural Science Foundation of China Grant No.11571009, Shanxi Scholarship Council of China under Grant No. 2015-032, Technological Innovation Programs of Higher Education Institutions in Shanxi Grant No. 2015121 and Applied Basic Research Programs of Shanxi Province Grant No. 2016021013

We study a population model with strong and weak Allee effect driven by internal noise and external noise. Firstly, a single-species population model with Allee effect under environmental colored noise is established, then stable and unstable states are analyzed and interpreted in biology. After that, stationary probability distribution (SPD) of population is derived based on Fokker-Planck equation. Next, mean first-passage time (MFPT) is defined in order to quantify the transition between extinction state and survival state with Allee effect. It is found that population will not extinct when weak Allee effect exists. It is not beneficial to survival of the population with the increase of Allee threshold no matter whether strong Allee effect or weak Allee effect. When strong Allee effect occurs, the correlation time of multiplicative noise plays a positive role in survival of population, while the correlation time of additive noise has a negative effect. Crucially, the phenomenon of resonant activation is firstly discovered in population dynamics with Allee effect. The conclusions we obtain can be applied to the further research of population dynamics in ecology.

Noise-induced decline and propagation of population in the delayed Malthus–Verhulst model

The effects of multiplicative and additive colored noises on decline and propagation processes of population in the delayed stochastic Malthus–Verhulst model are investigated by numerically computing and stochastically simulating. From the biological point of view, our results indicate that: the increasing correlation time of multiplicative noise strengthens the stability of population, and the correlation time of additive noise does not affect it. The increasing correlation time of multiplicative noise slows down the replacement of old individuals with young ones, while the increasing correlation time of additive noise with short delay time and the optimal correlation time of additive noise with long delay time quicken it.

Coherence resonance in a nonlinear neuronal models driven by correlated colored noise

The phenomenon of coherence resonance in a nonlinear integrate-and-fire neuronal model subject to correlated multiplicative synaptic and additive voltage-gated channel noise are investigated. Based on the adiabatic approximation theory and the unified colored approximation method，the analytic expression of the probability distribution of the first fire （FPD） and the coefficient of variation （CV） of the inter-spike interval of firing are obtained. It is shown that the FPD and the CV are functions of the intensity of the multiplication synaptic colored noise，the additive voltage-gated channel white noise，the correlation time of multiplicative noise and the strength of the correlation between noises. By choosing appropriate noise parameters，the phenomenon of coherence resonance can occur. Meanwhile，the effects of intensity of the multiplication synaptic noise，the additive voltage-gated channel noise，the correlation time of multiplicative noise and the strength of the correlation between noises on coherence resonance are discussed.

The mean first-passage time for an asymmetric bistable system driven by two colored noises

By means of an extended colored-noise approximation，we investigated the effects of asymmetry of the potential and noises on the mean first-passage time T+（xs1→xs2） and T-（xs2→xs1） in two opposite directions in an asymmetric bistable system （here xs1 and xs2 are stable points of the asymmetric bistable system）. Numerical results show that T+（xs1→xs2） decreases with increasing of τ1 （the correlation time of multiplicative noise） and τ2 （the correlation time of additive noise）. T-（xs2→xs1） increases with increasing of τ1 and τ2. The curves of T+（xs1→xs2） versus λ and T-（xs2→xs1） versus λ are single-peaked. T+（xs1→xs2） will increase when r increases，but T-（xs2→xs1） will decrease when r increases.

Parameter-induced stochastic resonance in an over-damped linear system

Stochastic resonance (SR) in an over-damped linear system subjected to an excitation of bias signal modulated noise with multiplicative and additive noises is investigated. We obtain the exact expressions of the first two moments and the signal-to-noise ratio (SNR) of the output by using linear-response theory. The SNR depends non-monotonically on the intensity and the correlation time of multiplicative noise, the correlation time of additive noise, the intensity of the cross noise between multiplicative and additive noise, as well as the external field frequency. The conventional SR, the SR in a broad sense and the bona fide SR are found in the system. The influences of the asymmetries of multiplicative and additive noise, the correlation rate of the cross noise, the intensity of additive noise, the amplitude of signal and the bias on the SNR are analyzed. Moreover, we pointed out that SR can be realized by tuning the system parameter with fixed noise, i.e., parameter-induced stochastic resonance (PSR) exists.