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Computational Mathematics and Modeling

, Volume 22, Issue 4, pp 444–453 | Cite as

A complete bifurcation diagram of nonlocal bifurcations of singular points in the Lorenz system

  • D. A. Kaloshin
  • N. A. Magnitskii
Article

For the system of Lorenz equations in the parameter space we construct a complete bifurcation diagram of all homoclinic and heteroclinic separatrix contours of singular points that exist in the system. These constructs include the existence surface of a homoclinic butterfly, the existence half-surface of homoclinic loops of saddle-focus separatrices, and the existence curve of a heteroclinic separatrix contour joining a saddle-node with two saddle-foci.

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Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • D. A. Kaloshin
  • N. A. Magnitskii

There are no affiliations available

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