Non-periodic bifurcations of one-dimensional maps
نویسندگان
چکیده
منابع مشابه
Bifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps
It is well known that dynamical systems defined by piecewise smooth functions exhibit several phenomena which cannot occur in smooth systems, such as for example, border collision bifurcations, sliding, chattering, etc. [di Bernardo et al., 2008]. One such phenomenon is the persistence of chaotic attractors under parameter perturbations, referred to as robust chaos [Banerjee et al., 1998]. In t...
متن کاملBorder collision bifurcations in one-dimensional linear-hyperbolic maps
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 beha...
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 کاملRelative periodic points of symplectic maps: persistence and bifurcations
In this paper we study symplectic maps with a continuous symmetry group arising by periodic forcing of symmetric Hamiltonian systems. By Noether’s Theorem, for each continuous symmetry the symplectic map has a conserved momentum. We study the persistence of relative periodic points of the symplectic map when momentum is varied and also treat subharmonic persistence and relative subharmonic bifu...
متن کاملCodimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps
We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2007
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385706000496