Multiple Predation on Prey Herding and Counteracting the Hunting

We introduce models for prey gathering in herds and subject to hunt by predators. Specifically, if in large numbers, the prey are able to defend themselves and adequately reduce the predators pressure, in line with other recent investigations in the literature. The findings extend previous results which indicate that in the presence of herding, prey may exhibit behaviors that differ from the ones predicted by classical quadratic predator-prey models. Indeed, with herding, persistent oscillations arise that are not induced by nonlinearities such as those of the Holling-Tanner model, originating limit cycles. The results are suitably compared with those of similar models, and the differences in behavior are highlighted.