Abstract
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.
Highlights
Dynamic models of strategic interaction between- two competitors are often represented by a map of the plane into itself T" (x+ 1, Y+ 1), defined as xt+l TI (1)Yt+ Tz(xt, Yt), where xt and Yt represent the state variables which characterize, at time t, the behavior of the two competitors
In this paper we investigate some particular properties of competition models with identical competitors
The global dynamical properties of the map T can be described by the method of critical curves and, in particular, the reinjection of the locally repelled trajectories can be described in terms of their folding action
Summary
- two competitors are often represented by a map of the plane into itself T" (xt, yt) (x+ 1, Y+ 1), defined as xt+l TI (xt, Yt) (1). In the models with onedimensional chaos synchronization the map (1) is often a noninvertible map of the plane, because its one-dimensional restriction f must be a noninvertible map in order to have chaotic motion along the invariant subspace A In this case, the global dynamical properties of the map T can be described by the method of critical curves (see [14, 24, 3]) and, in particular, the reinjection of the locally repelled trajectories can be described in terms of their folding action
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
