EFFECTS OF NOISE ON CYCLIC COMPETITIONS AMONG THREE SPECIES

2011 ◽  
Vol 25 (22) ◽  
pp. 3043-3052
Author(s):  
LINRU NIE ◽  
AILING GONG ◽  
DONGCHENG MEI
Keyword(s):  
Numerical Simulations ◽  
Stochastic Resonance ◽  
Spatial Correlation ◽  
Spatial Patterns ◽  
Multiplicative Noise ◽  
Correlation Coefficients ◽  
Volterra Model

The Lotka–Volterra model of cyclic competitions among three species with noise was investigated by numerical simulations. Our results indicate that the multiplicative noise is responsible for the alternately sinusoidal competitive oscillations of species, the optimizations of response of the system via stochastic resonance, the spatial patterns and the temporal oscillations of the spatial correlation coefficients.

Stochastic resonance and stability for an ecological vegetation growth system driven by colored noises and multiplicative signal

2016 ◽  
Vol 30 (24) ◽  
pp. 1650308 ◽  
Author(s):  
Kang-Kang Wang ◽  
Ya-Jun Wang ◽  
Jian-Cheng Wu
Keyword(s):  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
Periodic Signal ◽  
Expansion Process ◽  
Correlation Times ◽  
Vegetation Growth ◽  
Growth System ◽  
Speed Up ◽  
The Stability

In this paper, we investigate the steady-state properties and the transition rate for an ecological vegetation growth system induced by the terms of the colored multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can reduce the stability of the ecological system and slow down the development velocity of the vegetation, while two noise self-correlation times can increase the stability of the system and speed up the expansion process of the vegetation system. With respect to the stochastic resonance (SR) phenomenon caused by noise terms and a multiplicative weak periodic signal, the results show that the additive noise always enhances the SR effect, two noise self-correlation time terms can produce SR phenomenon, but play opposite roles in enhancing or inhibiting the SR effect under different parameter conditions. In particular, the two self-correlation times can keep up the maximum of the signal-to-noise ratio (SNR) invariant in specific situations. Analogously, the multiplicative noise can not only improve the SNR, but also restrain the SR phenomenon in different cases.

scholarly journals NOISE INDUCED PHENOMENA IN LOTKA-VOLTERRA SYSTEMS

2003 ◽  
Vol 03 (02) ◽  
pp. L177-L185 ◽  
Author(s):  
B. SPAGNOLO ◽  
A. FIASCONARO ◽  
D. VALENTI
Keyword(s):  
Time Evolution ◽  
Stochastic Resonance ◽  
Spatial Patterns ◽  
Discrete Model ◽  
Initial Conditions ◽  
External Noise ◽  
Competing Species ◽  
Interacting Species ◽  
Volterra Systems

We study the time evolution of two ecosystems in the presence of external noise and climatic periodical forcing by a generalized Lotka-Volterra (LV) model. In the first ecosystem, composed by two competing species, we find noise induced phenomena such as: (i) quasi deterministic oscillations, (ii) stochastic resonance, (iii) noise delayed extinction and (iv) spatial patterns. In the second ecosystem, composed by three interacting species (one predator and two preys), using a discrete model of the LV equations we find that the time evolution of the spatial patterns is strongly dependent on the initial conditions of the three species.

Impact of Time Delay and Cross-Correlated Gaussian Colored Noises on Dynamical Characteristics and Stochastic Resonance for a Metapopulation System

2020 ◽  
pp. 2150024
Author(s):  
Kang-Kang Wang ◽  
De-Cai Zong ◽  
Ya-Jun Wang ◽  
Sheng-Hong Li
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Resonant Peak ◽  
Noise Correlation ◽  
Ecological Stability ◽  
Correlation Times ◽  
Correlation Strength

In this paper, the regime shift behaviors between the prosperous state and the extinction state and stochastic resonance (SR) phenomenon for a metapopulation system subjected to time delay and correlated Gaussian colored noises are investigated. Through the numerical calculation of the modified potential function and the stationary probability density function (SPDF), one can make clearly the following results: Both multiplicative noise and noise correlation times can improve effectively the ecological stability and prolong the survival time of the system; while additive noise, time delay and noise correlation strength can weaken significantly the biological stability and speed up the extinction of the population. As for the signal-to-noise ratio (SNR), it is found that time delay, multiplicative noise and noise correlation strength can all impair the SR effect. Conversely, the two noise correlation times and additive noise are in favor of the improvement of the peak values of SNR. It is particularly worth mentioning that in the case of [Formula: see text], time delay [Formula: see text] and self-correlation time [Formula: see text] of the additive noise display exactly the opposite effect on the stimulation of the resonant peak in the SNR–[Formula: see text] plots.

A Novel Adaptive Stochastic Resonance Method Based on Tristable System and its Applications

2020 ◽  
pp. 2150004
Author(s):  
Gang Zhang ◽  
Chuan Jiang ◽  
Tian Qi Zhang
Keyword(s):  
Signal Detection ◽  
Stochastic Resonance ◽  
Piecewise Linear ◽  
Correlation Coefficients ◽  
Resonance Method ◽  
Resonance System ◽  
Signal Energy ◽  
Noise Energy ◽  
Novel Model ◽  
Output Snr

Stochastic resonance systems have the advantages of converting noise energy into signal energy, and have great potential in the field of signal detection and extraction. Aiming at the problems of the performance of classical stochastic resonance system whose model is not perfect enough and the correlation coefficients between parameters is too large to be optimized by algorithm, then a novel model of the tristable potential stochastic resonance system is proposed. The output SNR formula of the model is derived and analyzed, and the influence of its parameters on the model is clarified. Compared with the piecewise linear model by numerical simulation, the correctness of the formula and the superiority of the model are verified. Finally, the model and the classical tristable model are applied to bearing fault detection in which the genetic algorithm is used to optimize the parameters of the two systems. The results show that the model has better detection effects, which prove that the model has a strong potential in the field of signal detection.

Stochastic Resonance in FitzHugh-Nagumo Neural Model

2013 ◽  
Vol 415 ◽  
pp. 298-302
Author(s):  
Deng Rong Zhou ◽  
Jian Chun Gong ◽  
Dan Li
Keyword(s):  
Stochastic Resonance ◽  
Adiabatic Approximation ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Neural Model ◽  
System Parameters ◽  
Maximum Value ◽  
External Incentives ◽  
Delayed Time

Stochastic resonance is a non-linear phenomenon where the output response of the dynamic system reaches the maximum value under the joint action of a certain intensity of noises and external incentives. In this paper, the phenomenon of stochastic resonance in a FitzHugh-Nagumo neural (FHN) model is studied. For the case that the frequency of the HF signal is much higher than that of the LF signal, under the adiabatic approximation condition, the expression of the signal-to-noise ratio (SNR) with respect to the LF signal is obtained. It is shown that, the SNR is a non-monotonous function of the amplitude and frequency of the HF signal. In addition, the SNR varies non-monotonically with increasing the intensities of the multiplicative and additive noise, with increasing the delayed-time as well as increasing the system parameters of the FHN model. The influence of the correlation time of the colored multiplicative noise and the influence of the coupling strength between the multiplicative and additive noise on the SNR is discussed.

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