Determination of Crisis Parameter Values by Direct Observation of Manifold Tangencies

John C Sommerer, Celso Grebogi

Research output: Contribution to journalArticle

Abstract

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
Volume2
Issue number2
DOIs
Publication statusPublished - Jun 1992

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Periodic Points
Unstable
Geometric Algorithms
Unstable Manifold
Stable Manifold
Scaling Relations
Chaotic System
Tangent line
Chaotic systems
Demonstrate
Observation
Crisis
Context

Cite this

Determination of Crisis Parameter Values by Direct Observation of Manifold Tangencies. / Sommerer, John C; Grebogi, Celso.

In: International Journal of Bifurcation and Chaos, Vol. 2, No. 2, 06.1992, p. 383-396.

Research output: Contribution to journalArticle

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