engleski

Bursts in average lifetime of transients for chaotic logistic map with a hole

Chaotic transients are studied for a logistic map at control parameter r equal four, with an inserted narrow hole. We find that average lifetime tau of chaotic transients that are dependent on the hole position roughly follows the Frobenius-Perron semicircle pattern in most of the unit interval, but at the positions that correspond to the low period, 1, 2, 3, ... unstable periodic orbits of the logistic map at r equal four there are bursts of tau. An asymptotic relation between the Frobenius-Perron and Kantz-Grassberger average lifetimes, at these positions, is obtained and explained in terms of missing preimages determined from a transient time map. The addition of noise leads to the destruction of bursts of average lifetime.

classical chaos; logistic equation; nonlinearity

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