SOCIAL BEHAVIOR OF GROUP DEFENSE IN A PREDATOR–PREY SYSTEM WITH DELAY

Abstract

This paper proposes a mathematical model describing the dynamics of both Antarctic krill and Blue whale population where Antarctic krill species (prey) has group defense when they aggregate in herds in order to provide a self-defense from Blue whale species (predator). Firstly, a sufficient condition for the global asymptotical stability of the positive equilibrium is given using Poincaré–Bendixson theorem excluding periodic solution. Furthermore, we discuss the existence of Hopf-bifurcation and give criteria for stability switches through the study of a first-order exponential polynomial characteristic equation. Finally, some numerical simulations are given to illustrate our results.