Aquatic Ecology and Water Environment Safety

CLC number: O175.25

Qualitative Analysis and Numerical Simulation of a Predator-Prey Model for Invertebrate Predators in Aquatic Population Ecosystem

水生种群生态系统中具有无脊椎捕食者的捕食食饵模型定性分析与数值模拟

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China (宝鸡文理学院　数学与信息科学学院，　陕西　宝鸡721013)

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 20 April 2025

Abstract

The predation mechanism of invertebrates (e.g., Tortanus dextrilobatus) on plankton in aquatic population ecosystem is a significant research topic. In this paper, the interaction between invertebrates and plankton is simulated by a modified Leslie-Gower predator-prey model. Using the theory of reaction-diffusion equations, a priori estimate, existence, uniqueness and stability conditions of the positive steady state solution are established. Furthermore, numerical simulations are conducted to quantitatively analyze the dynamical behavior. The research shows that as long as the Allee effect constant satisfies the appropriate relationship and the growth rates of predator and prey are appropriately large, the predator and prey can not only coexist, but also the coexistence mode is unique and stable under low predation-rate. In addition, the numerical simulations show that the coexistence may be stable under high predation-rate. Meanwhile, with the increase of predation rate, the population density of predators will decrease.

摘要

无脊椎动物(例如溞溏水蚤)对水生种群生态系统中浮游生物的捕食机制是一个重要的研究课题。本文采用改进的Leslie-Gower捕食-食饵模型模拟了无脊椎动物和浮游生物之间的相互作用。利用反应扩散方程理论，建立了正稳态解的先验估计、存在性、惟一性和稳定性条件。此外，利用数值模拟定量分析了模型动力学行为。研究表明，只要Allee效应常数满足适当的关系、捕食者和食饵的生长速度适当大，捕食者和食饵不仅可以共存，而且在低捕食率下共存模式是惟一且稳定的。此外，数值模拟表明，在高捕食率下，也可能共存。同时，随着捕食率的增加，捕食者的种群密度会减小。