Mathematical Study About a Predator–Prey Model with Anti-predator Behavior

Species use their defense mechanisms to fight, kill or escape from predators. Each species shows its unique defense mechanism to avoid the predation. In this paper, we propose and analyze a three species predator–prey system with group defense mechanism. Conditions for boundedness and positivity of equilibrium points have been discussed. We establish conditions for stability of positive equilibrium points and periodic solutions via Hopf-bifurcation. The predator–prey system is numerically studied with the help of phase portrait, time evolution and bifurcation diagrams. Lyapunov exponent and sensitivity analysis ensure the chaotic behaviour of the model system. Period doubling and period halving bifurcations show dynamical complexities of the food chain system. This study suggests that the repercussion of better group defense by the intermediate predator is able to produce chaos in food chain models.