Analysis and simulation on dynamics of a pest-natural enemy model with additional food, pest-taxis and degeneracy

In this paper, we consider a pest-natural enemy model with additional food, pest-taxis and degeneracy. Firstly, in view of the regularity theory of elliptic equations and maximum principle, the asymptotic behaviors of positive solutions are investigated. We verify that when the maximum number of natural enemies that a unit volume can accommodate (caused by pest-taxis) is sufficiently large, or the quality or quantity of additional food is very poor or large, respectively, the model admits pest-free solution. Then, based on the bifurcation theory and stability theory, the existence and stability of bifurcation solutions are discussed. We obtain that the combination of additional food, pest-taxis and degeneracy can induce model to produce new positive solutions. Finally, we depict the control regions of pests by the bifurcation results. From a biological point of view, these results show that the combined introduction of additional food, pest-taxis and degeneracy not only induces model to generate new dynamics, but also has significant implications in controlling and eliminating pests.