Bifurcations and global dynamics in a toxicant-dependent aquatic population model
The study of the effects of environmental toxins such as lead, mercury, cadmium, etc., on ecosystems, is of great interest from both ecological and conservation points of view. In this talk, I present the dynamics of a toxin-dependent aquatic population model. The analytical and numerical studies show that population persistence is significantly affected by not only the environmental toxin level but also the depuration capability of the population. More interestingly, rich dynamics occur in the intermediate toxin concentrations, for instance, transient oscillations, hysteresis, heteroclinic orbits, and a codimension-two bifurcation. In addition, a regime of bistability exists where the population is doomed to extinction or survival, depending on the system's initial state. As a practical implication of the system, I investigate the toxic effects of methylmercury on rainbow trout. The developed theory in this work provides a sound theoretical foundation for understanding the population effect of toxicity. This is joint work with Qihua Huang (Southwest University, China) and Chunhua Shan (University of Toledo, USA).