@Article{AAM-34-4,
author = {Xinyu, Guan},
title = {Stability Analysis of a Lotka-Volterra Commensal Symbiosis Model Involving Allee Effect},
journal = {Annals of Applied Mathematics},
year = {2018},
volume = {34},
number = {4},
pages = {364--375},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {},
doi = {https://doi.org/2018-AAM-20584},
url = {https://global-sci.com/article/72728/stability-analysis-of-a-lotka-volterra-commensal-symbiosis-model-involving-allee-effect}
}