Eur. Phys. J. B 77, 273-279 (2010)
https://doi.org/10.1140/epjb/e2010-00239-6

Two competing species in super-diffusive dynamical regimes

¹ Dipartimento di Fisica e Tecnologie Relative, Group of Interdisciplinary Physics (http://gip.dft.unipa.it) , Università di Palermo and CNISM-INFM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy
² N.I. Lobachevsky State University, 23 Gargarin Ave., Nizhniy Novgorod, 603950, Russia

Corresponding authors: ^a angelolc@gip.dft.unipa.it - ^b valentid@gip.dft.unipa.it - ^c spagnolo@unipa.it

Received: 3 February 2010
Revised: 11 June 2010
Published online: 6 August 2010

Abstract

The dynamics of two competing species within the framework of the generalized Lotka-Volterra equations, in the presence of multiplicative α-stable Lévy noise sources and a random time dependent interaction parameter, is studied. The species dynamics is characterized by two different dynamical regimes, exclusion of one species and coexistence of both, depending on the values of the interaction parameter, which obeys a Langevin equation with a periodically fluctuating bistable potential and an additive α-stable Lévy noise. The stochastic resonance phenomenon is analyzed for noise sources asymmetrically distributed. Finally, the effects of statistical dependence between multiplicative noise and additive noise on the dynamics of the two species are studied.