WSEAS Transactions on Circuits and Systems
Print ISSN: 1109-2734, E-ISSN: 2224-266X
Volume 21, 2022
Global Attractivity of a Single Species Model with both Infinite Delay Merdan Type Allee effect
Authors: , ,
Abstract: This paper proposes and investigates a single-species model with infinite delay and Merdan- type Allee effect. The model takes the form $$\frac{dx}{dt}=x(a-bx-c\int_{-\infty}^{t}K(t-s)x(s)ds)\frac{x}{β-x}$$, where a, b, c, and β are all positive constants. The differential inequality theory and iterative method are used to obtain sufficient conditions that ensure the global attractivity of the system’s positive equilibrium. Our research shows that the Allee effect does not affect the final density of the species; however, the numerical simulations show that with the increase of the Allee effect, the system takes much time to the stale state.
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Keywords: Dynamical Systems, Systems Theory, Single species, Infinite delay, Global attractivity, Allee effect
Pages: 316-322
DOI: 10.37394/23201.2022.21.34