Simultaneous Effects of Primary and Secondary Toxicants on the Existence of Two competing Populations in an Aquatic Ecosystem: A Mathematical Analysis

Authors : Anita Chaturvedi, Vatsala G.A, O. P Misra, Babitha B S.

Volume/Issue : AAM – 2019

Google Scholar : https://goo.gl/DF9R4u

Scribd : https://bit.ly/2WSU90Y

Abstract : In this paper, the simultaneous effects of primary and secondary toxicants on the existence of two competing populations in an aquatic ecosystem has been studied and analysed using mathematical techniques and tools. A mathematical model is proposed to study the effect of primary toxicant and as well as secondary toxicants which is formed as a result of the presence of a chemical compound in the water of the aquatic body on the survival or extinction of the two competing populations. The model has been formulated using a system of non-linear differential equations. In this model, a separate differential equation has been considered for the formation of secondary toxicant as a result of the reaction of the primary toxicant with the chemical present in the water. The logistic growth population models for the competing species is considered and it has been assumed that the primary toxicant reduces the carrying capacity of the population and secondary toxicant reduces the specific growth rates of both the populations. The mathematical model proposed in this chapter has been analysed using stability theory.

Keywords : Toxicants, Logistic Growth Population Models, Competing Species, Stability Theory.

In this paper, the simultaneous effects of primary and secondary toxicants on the existence of two competing populations in an aquatic ecosystem has been studied and analysed using mathematical techniques and tools. A mathematical model is proposed to study the effect of primary toxicant and as well as secondary toxicants which is formed as a result of the presence of a chemical compound in the water of the aquatic body on the survival or extinction of the two competing populations. The model has been formulated using a system of non-linear differential equations. In this model, a separate differential equation has been considered for the formation of secondary toxicant as a result of the reaction of the primary toxicant with the chemical present in the water. The logistic growth population models for the competing species is considered and it has been assumed that the primary toxicant reduces the carrying capacity of the population and secondary toxicant reduces the specific growth rates of both the populations. The mathematical model proposed in this chapter has been analysed using stability theory.

Keywords : Toxicants, Logistic Growth Population Models, Competing Species, Stability Theory.