A Study of Verhulst’s Model with Gaussian
Correlated Noise

S.S. Rajput; S.S. Yadav

doi:https://doi.org/10.14445/22315373/IJMTT-V2I3P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 2 | Issue 3 | Year 2011 | Article Id. IJMTT-V2I3P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V2I3P502

A Study of Verhulst’s Model with Gaussian Correlated Noise

S.S. Rajput, S.S. Yadav

Abstract

The Verhulst’s differential equation is used to analyze cancer cell population in the existence of correlated white noise. We discuss the steady state properties of tumor cell growth and discuss the effect of correlated noise. We have obtained steady state probability function for tumor cell population from Fokker-Planck equation. The study reveals that as degree of correlation of the noise increases tumor cells died out.

Keywords

Verhulst differential equation, Stationary probability density function, Gaussin correlation noise

References

[1] Castro, F.; Wio, H.S.; Abramson, G. (1995): “Colored-noise problem: A Markovian interpolation procedure, Physical Review E, 52(1):159-164.
[2] Ali, B.Q.; Wang, X.J.; Liu, G.T.; Liu, L.G. (2003): “Correlated noise in a logistic model”, Physics Review E67, 022903(1-3).
[3] Zhong, W.R.; Shaho, Y.Z.; He, Z.H. (2006): “Influence of correlated noises on a growth of a tumor in a modified Verhulst’s model”, Scientific Journal on Random Processes in Physical, Biological and Technological systems, 6(4): L349-L358.
[4] Jin, S. and Qun, Z.S.: “Transitions in a logistic growth model induced by noise coupling and noise color”, Commun. Theor. Phys., 46: 175-182
[5] Liao, H.Y.; Ali, .Q.; Hu, L. (2007): “Effects of multiplicative colored noise on Bacteria growth”, Brazilian Journal of Physics, 37(3B): 1125-1128.
[6] Behera, A. and O’ Rourke, S.F.C. (2008): “The effect of correlated noise in a Gompertz tumor growth model”, Brazilian Journal of Physics, 38(2):272-278.
[7] Mei, D.C. and Du, L.C. (2009): “Effect of time delay in stationary properties of a logistic growth model with correlated noises”, Statistical Mechanics and its application, 389(6):1189-1196.
[8] Jing, T. AND Yong, C. (2010): “Effect of time delay on stochastic tumor growth”, CHN. PHYS. LETT. 27(3): 030502(1-4)

Citation :

S.S. Rajput, S.S. Yadav, "A Study of Verhulst’s Model with Gaussian Correlated Noise," International Journal of Mathematics Trends and Technology (IJMTT), vol. 2, no. 3, pp. 4-6, 2011. Crossref, https://doi.org/10.14445/22315373/IJMTT-V2I3P502