Title: Behaviour of generalised logistic equations on time scales

Authors: Kyle Kalail, Julia St. Goar, Paul Weber

Addresses: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA. ' Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA. ' Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA

Abstract: In this paper, we study the characteristics of generalised logistic and exponential functions on various time scales. The motivation behind this paper is that some populations are better modelled by exponential and logistic equations on a particular time scale. However, an unusual characteristic of some logistic equations on time scales is the possibility of producing negative output values, something that is impossible for a population. So the focus of this paper will be analysing the generalised logistic equation and creating necessary conditions such that the output of these equations on time scales remains greater than zero for all points in the time scale.

Keywords: time scales; logistic equations; exponential functions.

DOI: 10.1504/IJDSDE.2011.038505

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.248 - 266

Published online: 09 Feb 2011 *

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