Citation
K. Kubota et al., A study on the dynamics of a generalized logistic map, IEICE T FUN, E83A(3), 2000, pp. 524-531
Citations number
8
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
ISSN journal
09168508
→ ACNP
Volume
E83A
Issue
3
Year of publication
2000
Pages
524 - 531
Database
ISI
SICI code
0916-8508(200003)E83A:3<524:ASOTDO>2.0.ZU;2-1
Abstract
Nonlinear dynamics of x(n + 1) = lambda{4x(n)(1 - x(n))}(q) is studied in t
his paper. Different from the logistic map (q = 1), in the case of q < q(1)
= (root 33 - 3)/12 = 0.22871..., there exists subcritical bifurcation beca
use the Schwarzian derivative cannot preserve its sign at the fixed point.
Moreover, when q < q(2) = 0.17585... and lambda = 1.0, a stable period 1 or
bit appears due to stabilization of the non-zero fixed point. Intermittent
chaos due to the type 3 of intermittency is also found in this system.