De Pasquale F. and Spagnolo B.

Stochastic model of population dynamics
F. de Pasquale and B. Spagnolo
Dipartimento di Fisica, Università de L'Aquila, via Vetoio 67010 Coppito-L'Aquila, Italia

INFM, Unità di Palermo, and Dipartimento di Energetica ed Applicazioni di Fisica, Università di Palermo, Viale delle Scienze, I-90128, Palermo, Italia

Recent investigations has been done on modelling the idiotopic network of the immune system [1]. In this work we study the population dynamics of an ecosystem by means of a simple stochastic model: a N-species generalization of the Lotka-Volterra model with a Malthus-Verhulst type of self regulation mechanism. We consider mean field interaction between the species and a multiplicative noise to take into account the influence of the environment. The dynamical behaviour and the stability of the system in a zero- dimensional case [2] and with n-interacting species is investigated [3]. The effect of the noise and of the initial distribution of the populations on the stability-instability transition is analyzed.

1. H. Rieger, J. Phys. A 22 (1989) 3447; J.D. Farmer, N.H. Packard and A.S. Perelson, Physica D 22 (1986) 187.
2. S. Ciuchi, F. de Pasquale, B. Spagnolo, Phys. Rev. E 47 (1993) 3915.
3. S. Ciuchi, F. de Pasquale, B. Spagnolo, Self Regulation Mechanism of an Ecosystem in a Non Gaussian Fluctuation Regime, Preprint (1996).