Discrete Dynamics in Nature and Society
Volume 5 (2000), Issue 3, Pages 149-160

Global properties of symmetric competition models with riddling and blowout phenomena

Giant-italo Bischi1 and Laura Gardini1,2

1Istituto di Scienze Economiche, University of Urbino, Urbino 61029, Italy
2lstituto di Matematica “E. Levi“, Facoltà di Economia, University of Parma, Italy

Received 15 March 2000

Copyright © 2000 Giant-italo Bischi and Laura Gardini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper the problem of chaos synchronization, and the related phenomena of riddling, blowout and on–off intermittency, are considered for discrete time competition models with identical competitors. The global properties which determine the different effects of riddling and blowout bifurcations are studied by the method of critical curves, a tool for the study of the global dynamical properties of two-dimensional noninvertible maps. These techniques are applied to the study of a dynamic market-share competition model.