Stochastic Dynamical Behaviors for a Time-Delayed Insect Outbreak System with a Periodic Signal Subjected to Multiplicative and Additive Noises

2018 ◽  
Vol 17 (03) ◽  
pp. 1850025
Author(s):  
Kang-Kang Wang ◽  
Lin Ju ◽  
Zu-Run Xu ◽  
Sheng-Hong Li ◽  
Jian-Cheng Wu
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
The Other ◽  
Periodic Signal ◽  
Insect Growth ◽  
Double Peaks ◽  
Growth System ◽  
The Stability

In this paper, our aim is to investigate the steady state behaviors, the stochastic resonance (SR) phenomenon and the mean decline time for a biological insect growth system induced by the terms of time delay, the multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can both weaken the stability of the biological system and accelerate the depression process of the insect population, while time delay can strengthen the stability of the insect growth system and prolong the lifetime of the insect system. With respect to the SR phenomenon caused by time delay, noise terms and the weak periodic signal, the results show that some interesting dual peak phenomena for the signal-to-noise ratio (SNR) occur frequently. Specific contents are as follows: In SNR-[Formula: see text] plots, the additive noise intensity [Formula: see text] and time delay [Formula: see text] can easily induce the phenomenon of dual peaks, while in the SNR-[Formula: see text] plots, the multiplicative noise intensity [Formula: see text] and time delay [Formula: see text] can both reduce the SR effect distinctly. On the other hand, in the SNR-[Formula: see text] plots, when either of [Formula: see text] or [Formula: see text] takes a big value, the other plays a negative role in stimulating the SR phenomenon; while either of them takes a small value, the other can excite a significant effect of double peaks.

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.

Impact of Time Delay and Non-Gaussian Noise on Stochastic Resonance and Stability for a Stochastic Metapopulation System Driven by a Multiplicative Periodic Signal

2019 ◽  
Vol 18 (03) ◽  
pp. 1950017
Author(s):  
Kang-Kang Wang ◽  
Hui Ye ◽  
Ya-Jun Wang ◽  
Ping-Xin Wang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Multiplicative Noise ◽  
Periodic Signal ◽  
Population System ◽  
The Stability ◽  
Non Gaussian ◽  
Multiplicative Periodic Signal

In the present paper, the stability of the population system and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by the terms of time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal are investigated in detail. By applying the fast descent method, the unified colored noise approximation and the SR theory, the expressions of the steady-state probability function and the SNR are derived. It is shown that multiplicative non-Gaussian noise, the additive Gaussian noise and time delay can all weaken the stability of the population system, and even result in population extinction. Conversely, the two noise correlation times can both strengthen the stability of the biological system and contribute to group survival. In regard to the SNR for the metapopulation system impacted by the noise terms and time delay, it is revealed that the correlation time of the multiplicative noise can improve effectively the SR effect, while time delay would all along restrain the SR phenomena. On the other hand, although the additive noise and its correlation time can stimulate easily the SR effect, they cannot change the maximum of the SNR. In addition, the departure parameter from the Gaussian noise and the multiplicative noise play the opposite roles in motivating the SR effect in different cases.

Time delay and non-Gaussian noise-induced stochastic stability and stochastic resonance for a metapopulation system subjected to a multiplicative periodic signal

2018 ◽  
Vol 32 (27) ◽  
pp. 1850327 ◽  
Author(s):  
Kang-Kang Wang ◽  
Hui Ye ◽  
Ya-Jun Wang ◽  
Ping-Xin Wang
Keyword(s):  
Time Delay ◽  
Gaussian Noise ◽  
Correlation Time ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Periodic Signal ◽  
Colored Gaussian Noise ◽  
The Stability ◽  
Non Gaussian ◽  
Multiplicative Periodic Signal

In this paper, the stable state transformation and the effect of the stochastic resonance (SR) for a metapopulation system are investigated, which is disturbed by time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal. By use of the fast descent method, the approximation of the unified colored noise and the SR theory, the dynamical behaviors for the steady-state probability function and the SNR are analyzed. It is found that non-Gaussian noise, the colored Gaussian noise and time delay can all reduce the stability of the biological system, and even lead to the population extinction. Inversely, the self-correlation times of two noises can both increase the stability of the population system and be in favor of the population reproduction. As regards the SNR for the metapopulation system induced by the noise terms and time delay, it is discovered that time delay and the correlation time of the multiplicative noise can effectively enhance the SR effect, while the multiplicative noise and the correlation time of the additive noise would all the time suppress the SR phenomena. In addition, the additive noise can effectively motivate the SR effect, but not alter the peak value of the SNR. It is worth noting that the departure parameter from the Gaussian noise plays the diametrical roles in stimulating the SR effect in different cases.

scholarly journals Mean first-passage time of a tumor cell growth system with time delay and colored cross-correlated noises excitation

2017 ◽  
Vol 37 (2) ◽  
pp. 191-198 ◽  
Author(s):  
Shenghong Li ◽  
Yong Huang
Keyword(s):  
Time Delay ◽  
Noise Intensity ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Tumor Cell Growth ◽  
First Passage ◽  
Growth System ◽  
The Mean ◽  
Correlated Noises

In this paper, the mean first-passage time of a delayed tumor cell growth system driven by colored cross-correlated noises is investigated. Based on the Novikov theorem and the method of probability density approximation, the stationary probability density function is obtained. Then applying the fastest descent method, the analytical expression of the mean first-passage time is derived. Finally, effects of different kinds of delays and noise parameters on the mean first-passage time are discussed thoroughly. The results show that the time delay included in the random force, additive noise intensity and multiplicative noise intensity play a positive role in the disappearance of tumor cells. However, the time delay included in the determined force and the correlation time lead to the increase of tumor cells.

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.

STOCHASTIC RESONANCE FOR A METAPOPULATION SYSTEM SUBJECTED TO CORRELATED COLORED NOISES

2013 ◽  
Vol 27 (18) ◽  
pp. 1350136 ◽  
Author(s):  
KANG-KANG WANG ◽  
XIAN-BIN LIU ◽  
SHENG-HONG LI
Keyword(s):  
Stochastic Resonance ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
State Theory ◽  
Descent Method ◽  
Correlated Noise ◽  
Signal To Noise ◽  
System Parameters ◽  
Fast Descent

In the present paper, for a Levins metapopulation system that is driven by correlated colored noises, the phenomenon of stochastic resonance (SR) is investigated. Based on the two-state theory and by the use of fast descent method, the expression of the signal-to-noise ratio (SNR) is obtained. Via a numerical simulation, it is shown that the conventional SR occurs in the Levins model for the different values of system parameters. And furthermore, it is revealed that, under the different conditions that if the correlation intensities between the two noises are different, i.e. positive or negative, then all the effects of the addictive noise intensity, the multiplicative noise intensity, the correlated noise intensity and the correlation time on SNR are different.

THE RELAXATION TIME AND THE CORRELATION FUNCTION FOR A LOGISTIC GROWTH SYSTEM DRIVEN BY COLORED CROSS-CORRELATION NOISES

2008 ◽  
Vol 08 (02) ◽  
pp. L213-L228
Author(s):  
CAN-JUN WANG ◽  
DONG-CHENG MEI
Keyword(s):  
Correlation Function ◽  
Relaxation Time ◽  
Tumor Cell ◽  
Noise Intensity ◽  
Multiplicative Noise ◽  
Gaussian White Noise ◽  
Operator Method ◽  
Logistic Growth ◽  
Arbitrary Initial Condition ◽  
Growth System

The associated relaxation time Tc and the normalized correlation function C(s) are investigated in the logistic growth system, which is used to describe a tumor cell growth process, driven by two Gaussian white noise sources and the correlation between the additive and multiplicative noise. The expression of Tc and C(s), which is the function of noise parameters (additive noise intensity α, multiplicative noise intensity D, correlation intensity λ and correlation time τ), is obtained by using the projection operator method. After introducing noise intensity ratio, a dimensionless parameter R = α/D, and performing the numerical computations, the two case are analyzed: (1) In the growth case, λ and τ play opposite roles on the Tc and the C(s). It must emphasize that there is a minimal evolution velocity to appear and the tumor cell numbers is hard to evolve from an arbitrary initial condition to the maximum. (2) In the decay case, λ and τ play same roles on the Tc and the C(s). There is a maximal evolution velocity to appear. The noises induce different responses of tumor cells between the growth and decay case.

INVESTIGATION OF STOCHASTIC RESONANCE IN MONOSTABLE SYSTEMS

2008 ◽  
Vol 18 (09) ◽  
pp. 2833-2839 ◽  
Author(s):  
N. V. AGUDOV ◽  
A. V. KRICHIGIN
Keyword(s):  
Stochastic Resonance ◽  
Output Signal ◽  
Noise Intensity ◽  
Signal To Noise Ratio ◽  
Gaussian White Noise ◽  
Periodic Signal ◽  
Signal Power ◽  
Signal To Noise ◽  
Input Noise ◽  
Power Amplification

The phenomena of stochastic resonance is studied in overdamped nonlinear monostable systems driven by a periodic signal and Gaussian white noise. It is shown that the signal power amplification as a function of input noise intensity can be different depending on nonlinearity: it can monotonically grow, decrease and it can reach a maximum at certain value of the noise intensity. Nevertheless, the output signal to noise ratio is shown to be always a decreasing function of input noise intensity.

THE CRITICAL EFFECTS OF TIME DELAY AND NOISE CORRELATION ON STOCHASTIC RESONANCE IN AN ASYMMETRIC BISTABLE SYSTEM

2011 ◽  
Vol 25 (16) ◽  
pp. 1377-1391 ◽  
Author(s):  
ZHENG-LIN JIA ◽  
DONG-CHENG MEI
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Noise Intensity ◽  
Signal To Noise Ratio ◽  
State Theory ◽  
Bistable System ◽  
Noise Correlation ◽  
Small Delay ◽  
Correlation Strength ◽  
Two Peaks

We investigate the effects of time delay and noise correlation on the stochastic resonance induced by a multiplicative signal in an asymmetric bistable system. By the two-state theory and small delay approximation, the expression of the output signal-to-noise ratio (SNR) is obtained in the adiabatic limit. The results show that SNR as a function of the multiplicative noise intensity D shows a transition from two peaks to one peak with the decreasing of cross-correlation strength λ and the increasing of delay time τ. Moreover, there are the doubly critical phenomena for SNR versus λ and τ, and SNR versus D and α (additive noise intensity).

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