3 years ago

Bifurcation structures in a 2D exponential diffeomorphism with Allee effect

J. Leonel Rocha, Abdel-Kaddous Taha

Abstract

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.

Publisher URL: https://link.springer.com/article/10.1007/s11071-019-04759-3

DOI: 10.1007/s11071-019-04759-3

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