Rocha, J. LeonelTaha, Abdel-Kaddous2019-01-142019-01-142019-03ROCHA, 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. 3357-33740924-090X1573-269Xhttp://hdl.handle.net/10400.21/9319An 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.engAllee’s effect bifurcationFold and flip bifurcationsDiffeomorphismsContour lineLinha de contornoDobrar e virar bifurcaçõesjournal articlehttps://doi.org/10.1007/s11071-019-04759-3