LAUSR

ABSTRACT In the present article, we have made an attempt to control the population dynamics under the influence of additional food and prey refuge. We have analyzed dynamic behaviour of predator–prey interaction where predator biomass is subjected to exhibit Crowley-Martin functional response towards the source food in presence of high quality and high quantity of additional food. Elementary characteristic of the proposed system such as positivity, uniform boundedness and uniform persistence have been derived. Existence conditions and the stability criteria of all equilibriums have been studied. Next, we have discussed the existence of transcritical bifurcation around each of the equilibriums taking some meaningful parameter as bifurcation parameter. It has been noticed that quality and quantity of additional food supplied to the predator play an important role in the growth of predator. Moreover, we have investigated the impacts of two time delays, logistic delay and gestation delay. Numerical computations have been performed to validate our analytical findings using MATLAB.