Determination of Crisis Parameter Values by Direct Observation of Manifold Tangencies

John C Sommerer, Celso Grebogi

Research output: Contribution to journalArticle


We discuss an algorithm to find the parameter value at which a nonlinear, dissipative, chaotic system undergoes crisis. The algorithm is based on the observation that, at crisis, the unstable manifold of an unstable periodic point becomes tangent to the stable manifold of the same or another, related unstable periodic point. This geometric algorithm uses much less computation (or data) than estimating the critical parameter value by using the scaling relation for chaotic transients, τ~(p−pc)−γ. We demonstrate the algorithm in both numerical and experimental contexts.
Original languageEnglish
Pages (from-to)383-396
Number of pages14
JournalInternational Journal of Bifurcation and Chaos
Issue number2
Publication statusPublished - Jun 1992


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