LOGISTIC MAPPING WITH A TIME-DEPENDENT SYSTEM-PARAMETER AND ITS ATTRACTOR BASINS WITH SELF-SIMILAR STRUCTURE
2004 ◽
Vol 14
(07)
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pp. 2407-2416
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Keyword(s):
In this paper, logistic mapping with a time-dependent system-parameter (referred as "LMTD") is proposed. In various choices of time dependence, the periodic one has been tried in order to investigate the dynamical properties of LMTD. In certain parameter regions, two different attractors coexist depending on the initial values, for instances, two different chaotic attractors, two different periodic attractors, or two periodic/chaotic attractors. In addition, the whole configuration space of the initial values forms basins of attractions of which structures indicate self-similarity.