Browsing by Author "Chugunova, Marina Alexandrovna"
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Item Open Access Difference population equation with the variable Allee effect and periodic carrying capacity(2018-08-09) Chugunova, Marina Alexandrovna; Bates, Larry M.; Badescu, Alexandru M.; Liao, Wenyuan; Chruchill, Richard C.The subject of this research is the location, stability, and the basin of attraction for the equilibrium points and periodic solutions for the Ricker equation enhanced with the mechanism for both weak and strong types of the Allee effect and periodic carrying capacity. The research has shown that just an addition of one biological phenomenon to Ricker equation, namely, the Allee effect, significantly changes the necessary conditions for the equilibrium point of the equation to obtain stability. This also increases the range of the parameters which allow for the equilibrium solution or a cycle to remain globally asymptotically stable. It was shown that the p-periodic carrying capacity always generates the p-periodic solutions which can be global attractors. Embedding the mechanism for the strong Allee effect generates several basins of attraction with either an equilibrium point or a stable cycle as an attractor. Concavity was proven not necessary for the attenuant property of the cycle.