Catastrophe of riddling
نویسنده
چکیده
Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace. We find that, under arbitrarily small, deterministic perturbations, a riddled basin is typically destroyed and replaced by fractal ones, a catastrophe of riddling. We elucidate, based on analyzing unstable periodic orbits, the dynamical mechanism of the catastrophe. Analysis of the critical behaviors leads to the finding of a transient chaotic behavior that is different from those reported previously.
منابع مشابه
Catastrophic bifurcation from riddled to fractal basins.
Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace that usually results from a symmetry. In realistic applications of chaotic systems, however, there exists no perfect symmetry. The aim of this paper is to examine the consequences of symmetry-breaking on riddling. In particular, we consider smooth deterministic perturbations that destroy ...
متن کاملNoise-Induced Riddling in Chaotic Systems.
Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise even if the attractor is transversely unstable, and we obtain universal scaling laws...
متن کاملScaling laws for noise-induced temporal riddling in chaotic systems
Recent work has considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. The existence of invariant subspace often relies on certain symmetry of the system, which is, however, a nongeneric property as system defects and small rand...
متن کاملOn Riddling and Weak Attractors
We propose a general deenition for riddling of subset V of R m with nonzero Le-besgue measure and show that is appropriate for large class of dynamical systems. We introduce the concept of a weak attractor, a weaker notion than a Milnor attractor and use this to reexamine and classify riddled basins of attractors. We nd that basins of attraction can be partially riddled but if this is the case ...
متن کاملRiddling of Chaotic Sets in Periodic Windows
Previous investigations of riddling have focused on the case where the dynamical invariant set in the symmetric invariant manifold of the system is a chaotic attractor. A situation expected to arise commonly in physical systems, however, is that the dynamics in the invariant manifold is in a periodic window. We argue and demonstrate that riddling can be more pervasive in this case because it ca...
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:
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
دوره 62 4 Pt A شماره
صفحات -
تاریخ انتشار 2000