IJPAM: Volume 42, No. 2 (2008)

COMPETITIVE LOGISTIC NETWORKS WITH ADAPTATION

A. Raimondi$^1$, C. Tebaldi$^2$
$^{1,2}$DIMAT - Dipartimento di Matematica
Politecnico di Torino
24, Corso Duca degli Abruzzi, Torino, 10129, ITALY
$^1$e-mail: alessia.raimondi@polito.it
$^2$e-mail: claudio.tebaldi@polito.it


Abstract.We consider a network where the local activity level of each node is described by the logistic equation and the interaction among nodes take the form of competition, also including a mechanism of adaptation. We study here analytically the equilibria of such system, depending on the interaction strength and the size of the network, and we prove existence of classes of invariant subspaces which allow the introduction of a reduced model, where $n$ appears as parameter. One of such models, of four equations, gives complete account of all equilibria in the complete system.

Received: August 17, 2007

AMS Subject Classification: 37C75

Key Words and Phrases: complex systems, networks, logistic equation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2