Homoclinic bifurcation to a transitive attractor of Lorenz type

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, , Citation C Robinson 1989 Nonlinearity 2 495 DOI 10.1088/0951-7715/2/4/001

0951-7715/2/4/495

Abstract

The author proves that a cubic differential equation in three dimensions has a transitive attractor similar to that of the geometric model of the Lorenz equations. In fact, what is proved is that such an attractor results if a double homoclinic connection of a fixed point with a resonance condition among the eigenvalues is broken in a careful way.

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10.1088/0951-7715/2/4/001