Non-autonomous periodic systems with Allee effects |
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Authors: | Rafael Luís Saber Elaydi Henrique Oliveira |
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Institution: | 1. Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, Technical University of Lisbon , Lisbon, Portugal rafaelluis@netmadeira.com;3. Department of Mathematics , Trinity University , San Antonio, TX, USA;4. Department of Mathematics , Instituto Superior Técnico, Technical University of Lisbon , Lisbon, Portugal |
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Abstract: | A new class of maps called unimodal Allee maps are introduced. Such maps arise in the study of population dynamics in which the population goes extinct if its size falls below a threshold value. A unimodal Allee map is thus a unimodal map with three fixed points, a zero fixed point, a small positive fixed point, called threshold point, and a bigger positive fixed point, called the carrying capacity. In this paper, the properties and stability of the three fixed points are studied in the setting of non-autonomous periodic dynamical systems or difference equations. Finally, we investigate the bifurcation of periodic systems/difference equations when the system consists of two unimodal Allee maps. |
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Keywords: | unimodal Allee maps threshold point carrying capacity composition map stability bifurcation |
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