Global properties of symmetric competition models with riddling and blowout phenomena

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.