Advances in Difference Equations
Volume 2010 (2010), Article ID 457073, 15 pages
Research Article

A Discrete Equivalent of the Logistic Equation

Division of Applied Mathematics and Mechanics, Department of Engineering Sciences, University of Patras, 26500 Patras, Greece

Received 29 September 2010; Accepted 10 November 2010

Academic Editor: Claudio Cuevas

Copyright © 2010 Eugenia N. Petropoulou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A discrete equivalent and not analogue of the well-known logistic differential equation is proposed. This discrete equivalent logistic equation is of the Volterra convolution type, is obtained by use of a functional-analytic method, and is explicitly solved using the 𝑧 -transform method. The connection of the solution of the discrete equivalent logistic equation with the solution of the logistic differential equation is discussed. Also, some differences of the discrete equivalent logistic equation and the well-known discrete analogue of the logistic equation are mentioned. It is hoped that this discrete equivalent of the logistic equation could be a better choice for the modelling of various problems, where different versions of known discrete logistic equations are used until nowadays.