Fear effect exerted by carnivore in grassland ecosystem

Abstract

A four-dimensional mathematical model is formulated to explore the fear effect exerted by large carnivore in the grassland ecosystem. The model depicts the interactions among herbage, domestic herbivore, wild herbivore and large carnivore, which incorporates both direct predation and anti-predator mechanisms. The dynamic properties of the model are analytically investigated, including the dissipativity of solutions, and the existence and stability of different equilibria. Some numerical simulations are also presented to exhibit rich dynamical behaviors, such as various types of bistabilities, periodic oscillation and chaotic oscillation. The study reveals that the appropriate level of fear factors can stabilize the system and increase the density of herbage and domestic herbivore. The fear effect plays an important role in maintaining the balance of the grassland ecosystem and promoting the economy of human society.