Stochastic resonance in a time-delayed Logistic growth model driven by multiplicative periodic signal and multiplicative and additive noise

2011 ◽  
Author(s):  
Huimei Pan ◽  
Yurong Zhou
Keyword(s):  
Stochastic Resonance ◽  
Growth Model ◽  
Additive Noise ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Model Driven ◽  
Logistic Growth Model ◽  
Multiplicative Periodic Signal

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chunyan Bai ◽  
Luchun Du ◽  
Dongcheng Mei
Keyword(s):  
Stochastic Resonance ◽  
Growth Model ◽  
Noise Intensity ◽  
Critical Phenomenon ◽  
Fixed Ratio ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Logistic Growth Model ◽  
Multiplicative Periodic Signal ◽  
Correlated Noises

AbstractThe stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

Stochastic Resonance in a Time-Delayed Logistic Growth Model Driven by Periodic Signal and White Noise

2011 ◽  
Vol 117-119 ◽  
pp. 703-707
Author(s):  
Yu Rong Zhou ◽  
Chong Qiu Fang
Keyword(s):  
White Noise ◽  
Stochastic Resonance ◽  
Growth Model ◽  
Delay Time ◽  
Signal To Noise Ratio ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Logistic Growth Model ◽  
Noise Ratio

stochastic resonance; time-delayed Logistic growth model; signal-to-noise ratio Abstract. The stochastic resonance in a time-delayed Logistic growth model subject to correlated multiplicative and additive white noise as well as to multiplicative periodic signal is investigated. Using small time delay approximation, we get the expression of the signal-to-noise ratio (SNR). It is found that the SNR is a non-monotonic function of the system parameters, of the intensities of the multiplicative and additive noise, as well as of the correlation strength between the two noises. The effects of the delay time in the random force is in opposition to that of the delay time in the deterministic force.

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.

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

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.

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