Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems

Celso Grebogi, Edward Ott, James A. Yorke

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Abstract

The average lifetime of a chaotic transient versus a system parameter is studied for the case wherein a chaotic attractor is converted into a chaotic transient upon collision with its basin boundary (a crisis). Typically the average lifetime T depends upon the system parameter p via T∼|p−pc|−γ, where pc denotes the value of p at the crisis and we call γ the critical exponent of the chaotic transient. A theory determining γ for two-dimensional maps is developed and compared with numerical experiments. The theory also applies to critical behavior at interior crises.
Original languageEnglish
Pages (from-to)1284-1287
Number of pages4
JournalPhysical Review Letters
Volume57
Issue number11
DOIs
Publication statusPublished - 15 Sep 1986

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