When less is more: Partial control to avoid extinction of predators in an ecological model

Extinction of a species is one of the most dramatic processes in ecology. Here we use an extended version of the McCann-Yodzis three-species food chain model proposed by Duarte et al. (2009), where a cooperative hunting term was added to the original McCann-Yodzis model and where the three species coexist: resources, consumers and predators. We consider a situation for which a chaotic transient is present in the dynamics implying the predators extinction. Taking into account that the system is affected by external disturbances, we implement a new control method, the partial control method, with the goal of avoiding the extinction with a control applied smaller than the external disturbances of the system. We have also shown that the partial control method implies smaller controls.