Border collision bifurcations in one-dimensional linear-hyperbolic maps
نویسندگان
چکیده
In this paper we consider a continuous one-dimensional map, which is linear on one side of a generic kink point and hyperbolic on the other side. This kind of map is widely used in the applied context. Due to the simple expression of the two functions involved, in particular cases it is possible to determine analytically the border collision bifurcation curves that characterize the dynamic behaviors of the model. In the more general model we show that the steps to be performed are the same, although the analytical expressions are not given in explicit form. © 2010 IMACS. Published by Elsevier B.V. All rights reserved.
منابع مشابه
Border collision bifurcations in two-dimensional piecewise smooth maps
Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle-node, pitchfork, or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and clas...
متن کاملBorder Collision Bifurcations in n-Dimensional Piecewise Linear Discontinuous Maps
Abstract. In this paper we report some important results that help in analizing the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the plane of discontinuity. Earlier, Feigin had made a similar analysis for general n-dimensional piecewise smooth continuous maps. Proceeding along sim...
متن کاملBorder-Collision bifurcations in One-Dimensional Discontinuous Maps
We present a classification of border-collision bifurcations in one-dimensional discontinuous maps depending on the parameters of the piecewise linear approximation in the neighborhood of the point of discontinuity. For each range of parameter values we derive the condition of existence and stability of various periodic orbits and of chaos. This knowledge will help in understanding the bifurcat...
متن کاملRobust chaos and border-collision bifurcations in non-invertible piecewise-linear maps
This paper investigates border-collision bifurcations in piecewise-linear planar maps that are non-invertible in one region. Maps of this type arise as normal forms for grazing–sliding bifurcations in three-dimensional Filippovtype systems. A possible strategy is presented for classifying fixed and period-2 points, that are involved in such bifurcations. This allows one to determine a region of...
متن کاملCenter bifurcation for Two-Dimensional Border-Collision Normal Form
In this work we study some properties associated with the bordercollision bifurcations in a two-dimensional piecewise linear map in canonical form, related to the case in which a xed point of one of the linear maps has complex eigenvalues and undergoes a center bifurcation when its eigenvalues pass through the unit circle. This problem is faced in several applied piecewise smooth models, such ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Mathematics and Computers in Simulation
دوره 81 شماره
صفحات -
تاریخ انتشار 2010