Intermittency Reinjection in the Logistic Map

ELASKAR, SERGIO; DEL RÍO, EZEQUIEL; ELASKAR, SILVINA

Symmetry

MDPI

Año: 2022 vol. 14 p. 1 - 19

Just below a Period-3 window, the logistic map exhibits intermittency. Then, the third iterate of this map has been widely used to explain the chaotic intermittency concept. Much attention has been paid to describing the behavior around the vanished fixed points, the tangent bifurcation, and the formation of the characteristic channel between the map and the diagonal for type-I intermittency. However, the reinjection mechanism has not been deeply analyzed. In this paper, we studied thereinjection processes for the three fixed points around which intermittency is generated. We calculated the reinjection probability density function, the probability density of the laminar lengths, and thecharacteristic relation. We found that the reinjection mechanisms have broader behavior than the usually used uniform reinjection. Furthermore, the reinjection processes depend on the fixed point.