Chaos, Periodic Chaos, and the Random- Walk Problem

Details Chaos, Periodic Chaos, and the Random- Walk Problem Chaos, Periodic Chaos, and the Random- Walk Problem

Dec 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982phrvl..49.1801k&link_type=abstract

Physical Review Letters, Volume 49, Issue 25, December 20, 1982, pp.1801-1804

Physics

Condensed Matter

Statistical Mechanics

8

Classical Statistical Mechanics

Scientific paper

The authors have studied whether numerically generated sequences from the logistic parabola fb(x)=4bx(1-x) with b, x∈[0,1], for values of b, above the Feigenbaum critical value b∞, are truly chaotic or whether they are periodic but with exceedingly large periods and very long transients. Using the logistic parabola the authors calculate via Monte Carlo simulation the average walk length for trapping on a one-dimensional lattice with a centrosymmetric trap. Comparison with exact results suggests that the only "truly chaotic" sequence is the one for which b=1.

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