Global stability and bifurcation analysis on the dynamics of three interacting populations in prey-predator system

Abstract

A mathematical model was proposed and analysed to study the dynamics of a system of a prey, primary predator and a super predator in which the predators show Holing Type II functional response to their respective prey. The study substantially provides mechanism for improving the survivability of honeybee population and to halt the negative impact of Varroa-mite infestation on honeybee population by introducing Pseudoscorpion to serve as a super predator of Varroa-mite. Also, the study significantly shows the impact of virus on honeybee infested with virus-carrying Varroa-mite. The global stability analysis and Hopf-bifurcation of the interior steady state existence of the system are studied and explored. The analytical results matched with the numerical results of the model developed.