One-dimensional dynamics for a discontinuous map

Moorad Alexanian

Physica A: Statistical Mechanics and its Applications, 1992, vol. 181, issue 1, 53-68

Abstract: A discontinuous, two-parameter family of one-dimensional maps is shown to posses many of the features of the quadratic (“logistic”) map; for instance, a unique, twice differentiable maximum. However, paths may be chosen in the two-dimensional parameter space which give rise to a wealth of possible routes to chaos. In particular, paths may be found for the Feigenbaum route to chaos — period-doubling cascade of bifurcations — with a resulting single parameter in the map converging geometrically with a constant ω<δ=4.6692016…. Also, the approach to chaos may be more abrupt; for instance, from a stable periodic orbit of any period n directly to chaotic motion.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:181:y:1992:i:1:p:53-68

DOI: 10.1016/0378-4371(92)90196-W

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