Affiliation:
1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
2. School of Science, Ningxia Medical University, Yinchuan 750004, China
Abstract
<abstract><p>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 $ \Lambda = 0. $ When $ \Lambda < 0, $ the equilibrium is asymptotically stable, and when $ \Lambda > 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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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