Year: 2018
Author: Xinyu Guan
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 4 : pp. 364–375
Abstract
In this paper, we present a stability analysis of a Lotka-Volterra commensal symbiosis model subject to Allee effect on the unaffected population which occurs at low population density. By analyzing the Jacobian matrix about the positive equilibrium, we show that the positive equilibrium is locally asymptotically stable. By applying the differential inequality theory, we show that the system is permanent, consequently, the boundary equilibria of the system is unstable. Finally, by using the Dulac criterion, we show that the positive equilibrium is globally stable. Although Allee effect has no influence on the final densities of the predator and prey species, numeric simulations show that the system subject to an Allee effect takes much longer time to reach its stable steady-state solution, in this sense that Allee effect has unstable effect on the system, however, such an effect is controllable. Such an finding is greatly different to that of the predator-prey model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-AAM-20584
Annals of Applied Mathematics, Vol. 34 (2018), Iss. 4 : pp. 364–375
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Lotka-Volterra commensal symbiosis model Allee effect global stability.