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Full-Text Articles in Physical Sciences and Mathematics
An Economical Model With Allee Effect, Rafael Luis, Saber Elaydi, Henrique Oliveira
An Economical Model With Allee Effect, Rafael Luis, Saber Elaydi, Henrique Oliveira
Saber Elaydi
The Marx model for the profit rate r depending on the exploitation rate e and on the organic composition of the capital k is studied using a dynamical approach. Supposing both e(t) and k(t) are continuous functions of time we derive a law for r(t) in the long term. Depending upon the hypothesis set on the growth of k(t) and e(t) in the long term, r(t) can fall to zero or remain constant. This last case contradicts the classical hypothesis of Marx stating that the profit rate must decrease in the long term. Introducing a discrete dynamical system in the …
Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker
Population Models With Allee Effect: A New Model, Saber Elaydi, Robert J. Sacker
Saber Elaydi
In this paper we develop several mathematical models of Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model that is our focus of study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.
General Allee Effect In Two-Species Population Biology, G Livadiotis, Saber Elaydi
General Allee Effect In Two-Species Population Biology, G Livadiotis, Saber Elaydi
Saber Elaydi
The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar …