✦ LIBER ✦

Dynamic behaviours of 2∞ attractor and q-phase transitions at bifurcations in logistic map

✍ Scribed by P. Philominathan; S. Rajasekar

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 377 KB
Volume: 229
Category: Article
ISSN: 0378-4371
DOI: 10.1016/0378-4371(96)00014-3

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✦ Synopsis

Dynamic behaviours of the 2 ~° attractor at the accumulation of period doubling in the logistic map are studied by the sum of the local expansion rates Sn(xl) of nearby orbits. The variance ([S~ (x)] 2 ) and algebraic exponent fin (x 1 ) = S, (x 1)/In (n) exhibits self-similar structures. The critical bifurcations such as intermittency, band merging and crisis-sudden widening of the chaotic attractor are studied in terms of a q-weighted average A(q), ( -~< q < oo) of the coarse-grained local expansion rates /X of nearby orbitals.