The Dynamic Behavior (Effects) of Impulsive Toxicant Input on a Single-Species Population in a Small Polluted Environment

TL;DR

This paper develops a mathematical model to analyze how impulsive toxicant inputs affect the survival and extinction of a single-species population in a polluted environment, providing thresholds for population persistence.

Contribution

It introduces a new mathematical model incorporating pulse toxicant inputs and derives conditions for population survival or extinction.

Findings

Identifies the surviving threshold of the population.

Provides sufficient conditions for persistence and extinction.

Analyzes the impact of impulsive toxicant inputs on population dynamics.

Abstract

In this paper, we study a single-species population model with pulse toxicant input to a small polluted environment. The intrinsic rate of population is affected by environment and toxin in organisms. The toxin in organisms is influenced by toxin in environment and the food chain. A new mathematical model is derived. By the Pulse Compare Theorem, we find the surviving threshold of the population and obtain the sufficient conditions of persistence and extinction of the population.