Abstract
All processes in organisms, from the interaction of molecules to complex functions of the brain and other organs, obey physical laws. Mathematical modeling is an important step towards uncovering the organizational principles and dynamic behavior of biological systems.
In so far as the theorems of mathematics relate to reality, they are not certain, and in so far as they are certain they do not relate to reality.
Every thing should be made as simple as possible but not simpler.
Albert Einstein (1879–1955).
Biology is moving from being a descriptive science to being a quantitative science.
John Whitmarsh, National Inst. of Health, 2005 Joint AMS.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L. Barbalat, Systemes d’ equations differentielles d’oscillations nonlineaires. Rev. Roumaine Math. Pures. Appl. 4, 267–270 (1959)
L. Von Bertalanffy, A quantitative theory of organic growth. Hum. Biol. 10(2), 181–213 (1938)
A.A. Blumberg, Logistic growth rate functions. J. Theor. Biol. 21, 42–44 (1968)
T.C. Fisher, R.H. Fry, Tech. Forecast. Soc. Changes 3, 75 (1971)
K. Gopalsamy, M.R.S. Kulenovic, G. Ladas, On logistic equation with piecewise constant arguments. Differ. Integr. Equat. 4, 215–223 (1990)
K. Gopalsamy, X.Z. He, D.Q. Sun, Oscillation and convergence in a diffusive delay logistic equation. Math. Nach. 164, 219–237 (1993)
Y. Liu, W. Ge, Global attractivity in a delay “food-limited’ models with exponential impulses. J. Math. Anal. Appl. 287, 200–216 (2003)
Y. Muroya, Uniform persistence for Lotka–Volterra type delay differential systems. Nonlinear Anal. Real World Appl. 4, 689–710 (2003)
J. Sugie, On the stability of a population growth equation with time delay. Proc. Roy. Soc. Edenb. A 120, 179–184 (1992)
S. Tang, L. Chen, Global attractivity in a “food-limited” population model with impulsive effects. J. Math. Anal. Appl. 266, 401–419 (2002)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Agarwal, R.P., O’Regan, D., Saker, S.H. (2014). Logistic Models. In: Oscillation and Stability of Delay Models in Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-06557-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-06557-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06556-4
Online ISBN: 978-3-319-06557-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)