Analytic structure of the Lorenz system

Michael Tabor, J. Weiss

Research output: Contribution to journalArticle

109 Citations (Scopus)

Abstract

The solutions of the Lorenz system are investigated by examination of their complex-time singularities. It is found that the location and type of singularity that occurs for complex time is critical in determining the behavior of the real-time solution. By direct expansion of the solution at a singularity its structure is determined. In general, the solutions are multiple valued in the neighborhood of a singularity; a property that is intimately related to the nonintegrability of the system. A numerical investigation is made of the analytic structure of solutions exhibiting turbulent bursts and undergoing period-doubling bifurcations.

Original languageEnglish (US)
Pages (from-to)2157-2167
Number of pages11
JournalPhysical Review A
Volume24
Issue number4
DOIs
StatePublished - 1981
Externally publishedYes

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period doubling
bursts
examination
expansion

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Analytic structure of the Lorenz system. / Tabor, Michael; Weiss, J.

In: Physical Review A, Vol. 24, No. 4, 1981, p. 2157-2167.

Research output: Contribution to journalArticle

Tabor, Michael ; Weiss, J. / Analytic structure of the Lorenz system. In: Physical Review A. 1981 ; Vol. 24, No. 4. pp. 2157-2167.
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