After suggesting criteria to recognize a new system and a new attractor—and to make a distinction between them—the paper details the topological analysis of the “cord” attractor. This attractor, which resembles a cord between two leaves, is produced by a three-dimensional system that is obtained after a modification of the Lorenz-84 model for the global atmospheric circulation [L. A. Aguirre and C. Letellier, Phys. Rev. E 83, 066209 (2011)]. The nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe, that is, to a spiral Rössler attractor with negative and positive global $\pi$ twists. Due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable, this attractor qualifies as a challenging benchmark in nonlinear dynamics.

• Received 16 August 2011

DOI:https://doi.org/10.1103/PhysRevE.85.036204