An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise

¹  Imperial College, Faculty of Natural Sciences Flowers Building G24 - South Kensington, SW7 2AZ London, UK, EU
²  Center for Nonlinear Science, University of North Texas - P.O. Box 311427, Denton, TX 76203-1427, USA
³  Instituto de Alta Investigación, Universidad de Tarapacá - Casilla 6-D Arica, Chile
⁴  Departamento de Física Facultad de Ciencias Universidad de Tarapacá - Casilla 7-D Arica, Chile

Corresponding authors: gaquino@imperial.ac.uk mauroh69@libero.it hcalisto@uta.cl

Received: 18 October 2009
Accepted: 3 March 2010

Abstract

Logistic growth models are recurrent in biology, epidemiology, market models, and neural and social networks. They find important applications in many other fields including laser modelling. In numerous realistic cases the growth rate undergoes stochastic fluctuations and we consider a growth model with a stochastic growth rate modelled via an asymmetric Markovian dichotomic noise. We find an exact analytical solution for the probability distribution providing a powerful tool with applications ranging from biology to astrophysics and laser physics.