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Advisor(s)
Abstract(s)
An embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included.
Description
Keywords
Allee’s effect bifurcation Fold and flip bifurcations Diffeomorphisms Contour line Linha de contorno Dobrar e virar bifurcações
Citation
ROCHA, J. Leonel; TAHA, Abdel-Kaddous – Bifurcation structures in a 2D exponential diffeomorphism with Allee effect. Nonlinear Dynamics. ISSN 0924-090X. Vol. 95, N.º 4 (2019), pp. 3357-3374
Publisher
Springer