Stochastic resonance in the logistic growth model with time-modulated correlated noise

2012 ◽  
Vol 61 (12) ◽  
pp. 1932-1937
Author(s):  
Zhi-Qi Huang ◽  
Ya-Na Peng ◽  
Feng Guo
Keyword(s):  
Stochastic Resonance ◽  
Growth Model ◽  
Logistic Growth ◽  
Correlated Noise ◽  
Logistic Growth Model

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.

scholarly journals Correlated noise in a logistic growth model

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Bao-Quan Ai ◽  
Xian-Ju Wang ◽  
Guo-Tao Liu ◽  
Liang-Gang Liu
Keyword(s):  
Growth Model ◽  
Logistic Growth ◽  
Correlated Noise ◽  
Logistic Growth Model

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.

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