Bifurcations and global dynamics in a toxin-dependent aquatic population model
Related Experiment Video
Updated: Feb 17, 2026

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
Published on: January 31, 2020
Qihua Huang1, Gunog Seo2, Chunhua Shan3
1School of Mathematical and Statistical Sciences, Southwest University, Chongqing 400715, China.
Abstract:
The study of effects of environmental toxins on ecosystems is of great interest from both environmental and conservation points of view. In this paper, we present a global stability and bifurcation analysis of a toxin-dependent aquatic population model. Our analytical and numerical results show that both the environmental toxin level and the depuration capability of the population significantly affect the population persistence. The model exhibits a multifarious array of dynamics. While low levels of external toxin allow population persistence and high levels of toxin lead to an extirpation, intermediate toxin concentrations can produce very rich dynamics, such as transient oscillations, hysteresis, heteroclinic orbits, and a codimension-two bifurcation. In particular, a regime of bistability exists where the population is doomed to extinction or survival, depending on initial state of the system. As a practical implication of our study, the toxic effects of methylmercury on rainbow trout are scrutinized. The theory developed here provides a sound theoretical foundation for understanding the population effects of toxicity.
More Related Videos
Related Concept Videos
Population Growth
Modeling with Differential Equations
Growth Models with Integration: Problem Solving
Exponential Equations for Modeling Growth
Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

