A Method to calculate Basin bifurcation Sets for a Two-Dimensional Noninvertible Map
نویسندگان
چکیده
In this paper we propose a numerical method to calculate basin bifurcation sets in a parameter space. It is known that the basin bifurcations always result from the contact of a basin boundary with the critical curve segment. A numerical example for a two-dimensional quadratic noninvertible map is illustrated and new results of basin bifurcations are shown.
منابع مشابه
On the Fractal Structure of Basin Boundaries in Two-Dimensional Noninvertible Maps
In this paper we give an example of transition to fractal basin boundary in a two-dimensional map coming from the applicative context, in which the hard-fractal structure can be rigorously proved. That is, not only via numerical examples, although theoretically guided, as often occurs in maps coming from the applications, but also via analytical tools. The proposed example connects the two-dime...
متن کاملStudying basin bifurcations in nonlinear triopoly games by using 3D visualization
We consider three-dimensional discrete dynamical system, obtained by the iteration of a noninvertible map of , which simulates the time evolution of an oligopoly game with three competing firms. The model is characterized by the presence of several coexisting stable equilibria, each with its own basin of attraction. In this paper we face the question of the delimitation of the basins and the de...
متن کاملFrom the Box-within-a-Box bifurcation Structure to the Julia Set Part II: bifurcation Routes to Different Julia Sets from an Indirect Embedding of a Quadratic Complex Map
Part I of this paper has been devoted to properties of the different Julia set configurations, generated by the complex map TZ : z′ = z − c, c being a real parameter, −1/4 < c < 2. These properties were revisited from a detailed knowledge of the fractal organization (called “boxwithin-a-box”), generated by the map x′ = x − c with x a real variable. Here, the second part deals with an embedding ...
متن کاملComplex Patterns on the Plane: Different Types of Basin Fractalization in a Two-Dimensional Mapping
Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter λ of the system is modified. Complex patterns on the plane are visualized as a consequence of the basins’ bifurcations. According to the already established nomenclature in the literature, we present the relevant phenomenology organized in different scenarios: fracta...
متن کاملSynchronization, intermittency and critical curves in a duopoly game
The phenomenon of synchronization of a two-dimensional discrete dynamical system is studied for the model of an economic duopoly game, whose time evolution is obtained by the iteration of a noninvertible map of the plane. In the case of identical players the map has a symmetry property that implies the invariance of the diagonal x1x2, so that synchronized dynamics is possible. The basic questi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 10 شماره
صفحات -
تاریخ انتشار 2000