Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model

I. I. Ovsyannikov, D. V. Turaev

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous verification of one of the Shilnikov criteria for the birth of the Lorenz attractor; we also supply a proof for this criterion. The results are applied in order to give an analytic proof for the existence of a robust, pseudohyperbolic strange attractor (the so-called discrete Lorenz attractor) for an open set of parameter values in a 4-parameter family of 3D Henon-like diffeomorphisms.

Original languageEnglish
Pages (from-to)115-137
Number of pages23
JournalNonlinearity
Volume30
Issue number1
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes

Keywords

  • Henon map
  • Lorenz attractor
  • homoclinic butterfly
  • separatrix value

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model'. Together they form a unique fingerprint.

Cite this