Global properties of symmetric competition models with riddling and blowout phenomena

In this paper the problem of chaos synchronization, and the related phenome na of riddling, blowout and on-off intermittency, are considered for discre te time competition models with identical competitors. The global propertie s which determine the different effects of riddling and blowout bifurcation s are studied by the method of critical curves, a tool for the study of the global dynamical properties of two-dimensional noninvertible maps. These t echniques are applied to the study of a dynamic market-share competition mo del.