Analytical prediction of the transition to chaos in Lorenz equations
نویسندگان
چکیده
منابع مشابه
Visualizing the transition to chaos in the Lorenz system
The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This paper addresses the role of the global stable and unstable manifolds in organising the dynamics. More precisely, for the standard system parameters, the origin has a two-dimensional stable manifold and the other two equilibria ...
متن کاملNoise-induced Hopf-bifurcation-type sequence and transition to chaos in the lorenz equations.
We study the effects of noise on the Lorenz equations in the parameter regime admitting two stable fixed point solutions and a strange attractor. We show that noise annihilates the two stable fixed point attractors and evicts a Hopf-bifurcation-like sequence and transition to chaos. The noise-induced oscillatory motions have very well defined period and amplitude, and this phenomenon is similar...
متن کاملChaos in the Lorenz Equations: a Computer-assisted Proof
A new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with computer-assisted computations. As an application of these methods it is proven that for an explicit parameter value the Lorenz equations exhibit chaotic dynamics. Introduction The purpose of this...
متن کاملfrom linguistics to literature: a linguistic approach to the study of linguistic deviations in the turkish divan of shahriar
chapter i provides an overview of structural linguistics and touches upon the saussurean dichotomies with the final goal of exploring their relevance to the stylistic studies of literature. to provide evidence for the singificance of the study, chapter ii deals with the controversial issue of linguistics and literature, and presents opposing views which, at the same time, have been central to t...
15 صفحه اولMetastable Chaos: The Transition to Sustained Chaotic Behavior in the Lorenz Model
The system of equations introduced by Lorenz to model turbulent convective flow is studied here for Rayleigh numbers r somewhat smaller than the critical value required for sustained chaotic behavior. In this regime the system is found to exhibit transient chaotic behavior. Some statistical properties of this transient chaos are examined numerically. A mean decay time from chaos to steady flow ...
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: Applied Mathematics Letters
سال: 2010
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.12.012