Predator-prey models with cannibalism in prey

Abstract

Cannibalism in the predator-prey model is the study to show the interaction between prey and predator where the presence of cannibalism exists in both species in real life. Moreover, cannibalism is ubiquitous in natural communities and also among researchers who are interested in mathematical ecology. The predator-prey model system is modelled using ordinary differential equations to describe the dynamic behaviour of the systems. This study introduces the stage-structured models where the adult and juvenile prey species are considered. The purpose of the study is to analyse the effect of the stage-structured of prey cannibalism on the stability based on the concept of Lotka-Volterra in the predator-prey model. Thus, in this study, there are two cases are considered: prey cannibalism in the predator-prey model with predation on adult prey and model with predation on juvenile prey. The objectives of this research are (i) to formulate the concept of Lotka-Volterra in a predator-prey model, (ii) to analyse prey cannibalism in predator-prey model with predation on adult prey, (iii) to analyse the predator-prey in prey cannibalism with predation on juvenile prey, and (iv) to analyse the effect of stage-structured predator-prey model with cannibalism in prey on stability. In analysing the models, the stability of the equilibrium point is obtained and described by using the properties of the eigenvalues and the Routh-Hurwitz Criteria. Last but not least, numerical examples and graph analysis are given to illustrate the stability of equilibrium points.