Lorenz-like dynamics in a Lorenz-like family
by
Hiroshi Kokubu
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

In this talk, I will discuss dynamics and bifurcations of a family of three dimensional ODEs which contains, as its subfamilies, the Lorenz equations, the Rössler's 2nd equations and many other known families exhibiting Lorenz-like chaotic dynamics. I shall show that the family with appropriate choice of parameters contains a specific type of singularly degenerate heteroclinic cycle, from which geometric Lorenz attractors will bifurcate, among other things. Although not proven, one can also expect different dynamics such as Hénon-like chaotic dynamics as well as hooked Lorenz attractors which were recently studied by M. Viana and S. Luzzatto, and which are also observed in the original Lorenz equations with large r and small b as found in the Sparrow's book on the Lorenz equations. I will also comment on the relation between the Lorenz-like dynamics and the true Lorenz equations.

Date received: May 4, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahh-15.