Effects of Temperature on the Existence of Resource Based Predator-Prey System: Modelling and Stability Analysis .

Thermal pollutants include the waste heat chiefly from atomic, nuclear and thermal power plants, which adversely affect the aquatic environment. Coal fired or nuclear fuel-fired steam power plants are associated with the problem of thermal pollution. The study of the effects of temperature on the existence of resource based predatorprey system is carried out in the paper using mathematical model. The study has been conducted considering preypredator system in which the parameters like growth rate, death rate, carrying capacity and interaction coefficients are assumed to be the functions of temperature which itself is changing with time. In writing the model, a separate dynamical equation for the temperature is supplemented with the equations for prey-predator system. In this paper, the effect of temperature is assumed to occur due to the natural reasons such as seasonal or climatic changes and also as a result of the hot water discharge from the industries. The mathematical model to study the effects of temperature on the existence of resource based prey-predator species system is analyzed using stability theory for two feasible equilibrium points. It is found that the first positive equilibrium state which is unstable without diffusion may become stable by considering diffusion and advection. On the basis of this analysis, conditions for survival or extinction of the prey and predator populations have been derived.