Vertices in parameter space: Double crises which destroy chaotic attractors

Jason A. C. Gallas, Celso Grebogi, James A. Yorke

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


We report a new phenomenon observed along a crisis locus when two control parameters of physical models are varied simultaneously: the existence of one or several vertices. The occurrence of a vertex (loss of differentiability) on a crisis locus implies the existence of simultaneous sudden changes in the structure of both the chaotic attractor and of its basin boundary. Vertices correspond to degenerate tangencies between manifolds of the unstable periodic orbits accessible from the basin of the chaotic attractor. Physically, small parameter perturbations (noise) about such vertices induce drastic changes in the dynamics.

Original languageEnglish
Pages (from-to)1359-1362
Number of pages4
JournalPhysical Review Letters
Issue number9
Publication statusPublished - 30 Aug 1993


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