Eur. Phys. J. B 83, 409-414 (2011)
https://doi.org/10.1140/epjb/e2011-20493-2

Regular Article

Effects on generalized growth models driven by a non-Poissonian dichotomic noise

¹ Instituto de Alta Investigación IAI, Universidad de Tarapacá, Casilla 7- D Arica, Chile
² Departamento de Física Facultad de Ciencias Universidad de Tarapacá, Casilla 7- D Arica, Chile

^a e-mail: mauroh69@gmail.com

Received: 20 June 2011
Received in final form: 22 August 2011
Published online: 10 October 2011

Abstract

In this paper we consider a general growth model with stochastic growth rate modelled via a symmetric non-poissonian dichotomic noise. We find an exact analytical solution for its probability distribution. We consider the, as yet, unexplored case where the deterministic growth rate is perturbed by a dichotomic noise characterized by a waiting time distribution in the two state that is a power law with power 1 < μ < 2. We apply the results to two well-known growth models; Malthus-Verhulst and Gompertz.