Analytic structure of the Lorenz system

M. Tabor, J. Weiss

Research output: Contribution to journalArticlepeer-review

114 Scopus citations


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
Issue number4
StatePublished - 1981
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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