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Advisor(s)
Abstract(s)
This paper concerns the study of the Allee effect on the dynamical behavior of a new class of generalized logistic maps. The fundamentals of the dynamics of this 4-parameter family of one-dimensional maps are presented. A complete classification of the nature and stability of its fixed points is provided. The main results relate to the Allee effect bifurcation: a new type of bifurcation introduced for this class of unimodal maps. A necessary and sufficient condition so that the Allee fixed point is a snap-back repeller is established. In addition, in the parameters space is defined an Allee's effect region, which determines the existence of an essential extinction for the generalized logistic maps. Local and global bifurcations of generalized logistic maps are investigated.
Description
Keywords
Generalized logistic maps Allee's effect bifurcation Snap-back repeller bifurcation Essential extinction
Citation
ROCHA, J. Leonel; TAHA, Abdel-Kaddous – Allee's effect bifurcation in generalized logistic maps. International Journal of Bifurcation and Chaos. ISSN 0218-1274. Vol. 29, N.º 3 (2019), pp. 1950039-1- 1950039-19
Publisher
World Scientific Publishing