Is the Hénon attractor chaotic?
نویسندگان
چکیده
By performing a systematic study of the Hénon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Hénon attractor-the attractor of the Hénon map existing for the classical parameter values-is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if the latter were true, it would be practically impossible to establish this by computing trajectories of the map.
منابع مشابه
Attractor Based Analysis of Centrally Cracked Plate Subjected to Chaotic Excitation
The presence of part-through cracks with limited length is one of the prevalent defects in the plate structures. Due to the slight effect of this type of damages on the frequency response of the plates, conventional vibration-based damage assessment could be a challenging task. In this study for the first time, a recently developed state-space method which is based on the chaotic excitation is ...
متن کاملبهبود بازشناسی مقاوم الگو در شبکه های عصبی بازگشتی جاذب از طریق به کارگیری دینامیک های آشوب گونه
In this paper, two kinds of chaotic neural networks are proposed to evaluate the efficiency of chaotic dynamics in robust pattern recognition. The First model is designed based on natural selection theory. In this model, attractor recurrent neural network, intelligently, guides the evaluation of chaotic nodes in order to obtain the best solution. In the second model, a different structure of ch...
متن کاملChaotic dynamics of three - dimensional Hénon maps that originate from a homoclinic bifurcation
We study bifurcations of a three-dimensional diffeomorphism, g 0 , that has a quadratic homoclinic tangency to a saddle-focus fixed point with multipliers (λe iϕ , λe −iϕ , γ), where 0 < λ < 1 < |γ| and |λ 2 γ| = 1. We show that in a three-parameter family, g ε , of dif-feomorphisms close to g 0 , there exist infinitely many open regions near ε = 0 where the corresponding normal form of the fir...
متن کاملDivergence measure between chaotic attractors.
We propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors. This measure is defined in terms of a generalized entropy. We illustrate our procedure by considering the effect of additive noise in the well known Hénon attractor. Finally, we show how our approach allows one to detect nonstationary events in a time series.
متن کاملWaiting time paradox applied to transient times
When working with chaotic systems, the average length of a transient phase before a particular event occurs is often required. Examples of this include the transient phase before a control mechanism can be activated @1,2# or the length of a chaotic transient after a crisis has occurred @3#. In both cases, the transient occurs before iterates fall into a small region. For controlling chaos, this...
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:
- Chaos
دوره 25 3 شماره
صفحات -
تاریخ انتشار 2015