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Bifurcations and global dynamics in a toxin-dependent aquatic population model
Qihua Huang1, Gunog Seo2, Chunhua Shan3
1School of Mathematical and Statistical Sciences, Southwest University, Chongqing 400715, China.
Mathematical Biosciences
|December 7, 2017
Summary
Environmental toxins impact aquatic populations, with intermediate concentrations causing complex dynamics like bistability. Understanding these effects is crucial for conservation and managing toxic substances like methylmercury.
Area of Science:
- Ecotoxicology
- Mathematical Biology
- Environmental Science
Background:
- Environmental toxins pose significant risks to ecosystems.
- Understanding toxin effects on aquatic populations is vital for conservation.
- Previous models often simplify complex population dynamics under toxicant exposure.
Purpose of the Study:
- To analyze the global stability and bifurcation of a toxin-dependent aquatic population model.
- To investigate how environmental toxin levels and population depuration affect population persistence.
- To explore the rich dynamics arising from intermediate toxin concentrations.
Main Methods:
- Global stability analysis
- Bifurcation analysis
- Numerical simulations
- Mathematical modeling of population dynamics
Main Results:
- Population persistence is significantly influenced by toxin levels and depuration rates.
- Intermediate toxin concentrations lead to complex dynamics, including transient oscillations, hysteresis, and bistability.
- A codimension-two bifurcation was identified, indicating critical shifts in population behavior.
- Bistability demonstrates that populations can either persist or face extinction based on initial conditions.
Conclusions:
- The developed model provides a theoretical foundation for understanding population-level effects of environmental toxins.
- The study highlights the critical role of toxin concentration in determining population fate.
- Findings have practical implications for managing toxic substances, exemplified by methylmercury's effects on rainbow trout.
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