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

P. Philominathan and S. Rajasekar

Physica A: Statistical Mechanics and its Applications, 1996, vol. 229, issue 2, 244-254

Abstract: 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(x1) of nearby orbits. The variance 〈[Sn(x)]2〉 and algebraic exponent ßn(x1) = Sn(x1)/ln(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 Λ(q), (− ∞ < q < ∞) of the coarse-grained local expansion rates Λ of nearby orbitals.

Keywords: Logistic map; Bifurcations; Local expansion rates and q-phase transitions (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:229:y:1996:i:2:p:244-254

DOI: 10.1016/0378-4371(96)00014-3

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