Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems

Celso Grebogi, Edward Ott, James A. Yorke

Research output: Contribution to journalArticle

221 Citations (Scopus)

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

Cite this

Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems. / Grebogi, Celso; Ott, Edward; Yorke, James A.

In: Physical Review Letters, Vol. 57, No. 11, 15.09.1986, p. 1284-1287.

Research output: Contribution to journalArticle

Grebogi, Celso ; Ott, Edward ; Yorke, James A. / Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems. In: Physical Review Letters. 1986 ; Vol. 57, No. 11. pp. 1284-1287.
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