Structure analysis of the Lorenz-84 chaotic attractor

The structure of the Lorenz-84 attractor is investigated in this study. Its dynamics belonging to weakly dissipative chaos, classical approaches cannot be used to analyze its structure. The color tracer mapping is introduced for this purpose and used to extract the three-dimensional structure of the attractor. The analysis shows that the attractor is a nontrivial case of toroidal chaos: it is organized around a period-2 cavity. Moreover, the structure reveals a new mechanism generating chaos in the attractor: a multidirectional stretching. The attractor structure is then artificially represented on a two-dimensional branched manifold, and its validation is performed using a set of periodic orbits previously extracted.