Period Doubling in the Rössler System - A Computer Assisted Proof
نویسندگان
چکیده
Using rigorous numerical methods we validate a part of the bifurcation diagram for a Poincaré map of the Rössler system [26] the existence of two period doubling bifurcations and the existence of a branch of period two points connecting them. Our approach is based on the LyapunovSchmidt reduction and uses the C-Lohner algorithm [31] to obtain rigorous bounds for the Rössler system.
منابع مشابه
Period Doubling in Area-Preserving Maps: An Associated One Dimensional Problem
It has been observed that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in a computer-assisted proof of existence of an area-preserving map with orbits of all binary periods in [EKW1] and [EKW2]. As it is the case with all non-trivial universality problems in non-dissipative systems in...
متن کاملDynamics of the Universal Area-preserving Map Associated with Period Doubling: Stable Sets
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R. A renormalization approach has been used in (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” areapreserving map F∗ — a map with orbits of all binary periods 2 , k ∈ N. In this paper, we consider infinitely re...
متن کاملPeriod Doubling Renormalization for Area-Preserving Maps and Mild Computer Assistance in Contraction Mapping Principle
A universal period doubling cascade analogous to the famous FeigenbaumCoullet-Tresser period doubling has been observed in area-preserving maps of R. Existence of the “universal” map with orbits of all binary periods has been proved via a renormalization approach in (Eckmann et al 1984) and (Gaidashev et al 2011). These proofs use “hard” computer assistance. In this paper we attempt to reduce c...
متن کاملDynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of R2. A renormalization approach has been used in (Eckmann et al 1982) and (Eckmann et al 1984) in a computer-assisted proof of existence of a “universal” area-preserving map F∗ — a map with orbits of all binary periods 2k, k ∈ N. In this paper, we consider maps in som...
متن کاملChaotic neuron clock
A chaotic model of spontaneous (without external stimulus) neuron firing has been analyzed by mapping the irregular spiking time-series into telegraph signals. In this model the fundamental frequency of chaotic Rössler attractor provides (with a period doubling) the strong periodic component of the generated irregular signal. The exponentially decaying broad-band part of the spectrum of the Rös...
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:
- Foundations of Computational Mathematics
دوره 9 شماره
صفحات -
تاریخ انتشار 2009