Models for the effect of toxicant in single-species and predator-prey systems

Abstract

Models of single-species and predator-prey systems in a polluted closed environment are developed and partially analyzed. Three cases are considered: a single influx of toxicant, a constant influx of toxicant, and a periodic pollution of the environment. In the case of single-species growth we are able to determine some local and global dynamics. In the case of predator-prey systems, we investigate the existence of steady states for a small constant influx of toxicant.

A Model for the Effect of Toxicant on a Three Species Food-Chain System with "Food-Limited" Growth of Prey Population

“…In the model, it is assumed that the growth rate and the carrying capacity of prey is negatively affected by environmental toxicant [19]. Toxicant is transferred to intermediate predator and top predator populations through food chain pathways.…”

Optimum Control for Spread of Pollutants through Forest Resources

“…Some researchers have studied the mathematical model for the effects of industrialization and pollution on forest resources. [10] studied the models for the effect of toxicant in single-species and predator-prey system. [11] analysed the modeling effect of an intermediate toxic product formed by uptake of a toxicant on plant biomass.…”

On the stability and Hopf-bifurcation of a multi-delayed competitive population system affected by toxic substances with imprecise biological parameters

“…The deterministic dynamic models with the effect of toxic substances on various ecosystems is studied by Hallam et al (1983a, b), Hallam and Luna (1984), Luna and Hallam (1987), Freedman and Shukla (1991), Ghosh et al (2002), He and Wang (2007), Das et al (2009) and many others. Researchers, in course of their study over the effect and nature of the toxic elements come to an important observation that the enhanced population of one species might affect or control the growth of another or several other species through the production of allelopathic toxins or stimulants, thus influencing seasonal succession (Rice 1984).…”