Global Bifurcation Analysis of the Lorenz System

Volume 7, Issue 6, pp 429--434 http://dx.doi.org/10.22436/jnsa.007.06.06

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Authors

Valery A. Gaiko - United Institute of Informatics Problems, National Academy of Sciences of Belarus, Surganov Str. 6, Minsk 220012, Belarus.

Abstract

We carry out the global bifurcation analysis of the classical Lorenz system. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor is not clear completely yet, and the most important question at present is to understand the bifurcation scenario of chaos transition in this system. Using some numerical results and our bifurcational geometric approach, we present a new scenario of chaos transition in the Lorenz system.

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Keywords

• Lorenz system
• bifurcation
• singular point
• limit cycle
• chaos.

MSC

•  34C28
•  37D45
•  37G35

References

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