Stability and Stochastic Resonance for a Time-Delayed Cancer Development System Subjected to Noises and Multiplicative Periodic Signal

2017 ◽  
Vol 16 (03) ◽  
pp. 1750022 ◽  
Author(s):  
Kang-Kang Wang ◽  
Ya-Jun Wang ◽  
Sheng-Hong Li
Keyword(s):  
Time Delay ◽  
Cancer Cells ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Critical Role ◽  
State Theory ◽  
Cancer Development ◽  
Periodic Signal ◽  
Development System ◽  
Multiplicative Periodic Signal

In this paper, the stability and the phenomenon of stochastic resonance (SR) for a stochastic time-delayed cancer development system that is induced by the multiplicative periodic signal, the multiplicative and the additive noises are investigated. By using the fast descent method, small time delay method and the two-state theory, the expressions of the steady state probability distribution function and the signal-to-noise ratio (SNR) are obtained. Numerical results reflect that the multiplicative and additive noise always restrain the diffusion of the cancer cells. Whereas, the time delay can not only control the spread of the tumor cells, but also suppress the extinction of cancer cells. Meanwhile, the conventional SR occurs in the tumor cell growth model under the excitation of different noises and time delay. In conclusion, the multiplicative noise always plays a critical role in restraining SR, a smaller additive noise can stimulate the SR, but the larger additive noise can weaken the SR and SNR. In particular, the time delay displays relatively complicated effects on the SR phenomenon of the system. It plays different roles in motivating or suppressing SR under the different conditions of parameters.

Stochastic resonance in a time-delayed tumor cell growth system driven by additive and multiplicative noises

2018 ◽  
Vol 32 (22) ◽  
pp. 1850259 ◽  
Author(s):  
Gang Zhang ◽  
Jiabei Shi ◽  
Tianqi Zhang
Keyword(s):  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
State Theory ◽  
Periodic Signal ◽  
Tumor Cell Growth ◽  
System Parameters ◽  
Growth System

In this paper, the stochastic resonance (SR) phenomenon in a time-delayed tumor cell growth system subjected to a multiplicative periodic signal, the multiplicative and additive noise is investigated. By applying the small time-delay method and two-state theory, the expressions of the mean first-passage time (MFPT) and signal-to-noise ratio (SNR) are obtained, then, the impacts of time delay, noise intensities and system parameters on the MFPT and SNR are discussed. Simulation results show that the multiplicative and additive noise always weaken the SR effect; while time delay plays a key role in motivating the SR phenomenon when noise intensities take a small value, it will restrain SR phenomenon when noise intensities take a large value; the cycle radiation amplitude always plays a positive role in stimulating the SR phenomenon, while, system parameters play different roles in motivating or suppressing SR under the different conditions of noise intensities.

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.

Stochastic resonance in an array of integrate-and-fire neurons with threshold

2018 ◽  
Vol 32 (16) ◽  
pp. 1850169 ◽  
Author(s):  
Bingchang Zhou ◽  
Qianqian Qi
Keyword(s):  
Stochastic Resonance ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Array Size ◽  
Periodic Signal ◽  
Signal Parameter ◽  
Input Noise ◽  
Integrate And Fire ◽  
Noisy Input ◽  
Better Than

We investigate the phenomenon of stochastic resonance (SR) in parallel integrate-and-fire neuronal arrays with threshold driven by additive noise or signal-dependent noise (SDN) and a noisy input signal. SR occurs in this system. Whether the system is subject to the additive noise or SDN, the input noise [Formula: see text] weakens the performance of SR but the array size N and signal parameter [Formula: see text] promote the performance of SR. Signal parameter [Formula: see text] promotes the performance of SR for the additive noise, but the peak values of the output signal-to-noise ratio [Formula: see text] first decrease, then increase as [Formula: see text] increases for the SDN. Moreover, when [Formula: see text] tends to infinity, for the SDN, the curve of [Formula: see text] first increases and then decreases, however, for the additive noise, the curve of [Formula: see text] increases to reach a plain. By comparing system performance with the additive noise to one with SDN, we also find that the information transmission of a periodic signal with SDN is significantly better than one with the additive noise in limited array size N.

Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection

2019 ◽  
Vol 33 (28) ◽  
pp. 1950341 ◽  
Author(s):  
Lifang He ◽  
Dayun Hu ◽  
Gang Zhang ◽  
Siliang Lu
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Random Force ◽  
Small Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Bearing Fault ◽  
Strength Formula ◽  
Time Delayed Feedback

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters [Formula: see text], [Formula: see text], asymmetry parameter [Formula: see text], time delay [Formula: see text], strength [Formula: see text] of the time-delayed feedback, noise intensities [Formula: see text] and [Formula: see text] of multiplicative and additive noise, and correlation strength [Formula: see text] between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results.

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.

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