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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 597012, 6 pages
http://dx.doi.org/10.1155/2014/597012
Research Article

Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model

1Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá, 1000000 Arica, Chile
2Escuela Universitaria de Ingeniería Eléctrica-Electrónica, Universidad de Tarapacá, 1000000 Arica, Chile
3Instituto de Alta Investigación IAI, Universidad de Tarapacá, 1000000 Arica, Chile

Received 8 January 2014; Revised 23 April 2014; Accepted 5 May 2014; Published 4 June 2014

Academic Editor: Klaus Kirsten

Copyright © 2014 Héctor Calisto et al. 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.

Abstract

We consider a generalized Malthus-Verhulst model with a fluctuating carrying capacity and we study its effects on population growth. The carrying capacity fluctuations are described by a Poissonian process with an exponential correlation function. We will find an analytical expression for the average of a number of individuals and show that even in presence of a fluctuating carrying capacity the average tends asymptotically to a constant quantity.