WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 22, 2023
Stability Analysis of a Single Species Model with Allee Effect and Density Dependent Birth Rate
Authors: , ,
Abstract: A single species model with Allee effect and density-dependent birth rate
$$\frac{\mathrm{d} x }{\mathrm{d} t}x(\frac{a}{b+cx}-d-ex)\frac{x}{b+x} $$
is proposed and studied in this paper, where a, b, c, d, e and β are all positive constants. Sufficient conditions
which ensure the system admits a unique globally stable positive equilibrium are obtained. Numeric simulations
show that with the increasing Alee effect, the system takes a much longer time to reach its stable steady-state
the solution, however, Allee effect has no influence on the final density of the species.