@article{Gong2023, 
author = {Wei Gong and Zhanping Wang},
title = {Stability of nonlinear population systems with individual scale and migration},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {1},
pages = {125-147},
keywords = {population model, polluted environment, individual scale, equilibrium solution, stability},
url = {https://www.sciopen.com/article/10.3934/math.2023006},
doi = {10.3934/math.2023006},
abstract = {In this paper, we study the stability of a nonlinear population system with a weighted total size of scale structure and migration in a polluted environment, where fertility and mortality depend on the density in different ways. We first prove the existence and uniqueness of the equilibrium point via a contraction mapping and give the expression for the equilibrium point. Some conditions for asymptotic stability and instability are presented by means of a characteristic equation. When the effect of density restriction on mortality is not considered, the threshold value of equilibrium stability can be obtained as    Λ  =  0. When    Λ  <  0  , the equilibrium is asymptotically stable, and when    Λ  >  0  , the equilibrium is unstable. In addition, the upwind difference method is used to discrete the model, and two examples are given to show the evolution of species.}
}