Dynamics of a mutualism model with saturated response

摘要

This paper considers a lattice version of mutualistic model of two species. The model has a form similar to that of Lotka–Volterra equations, while the functional response is described by a Holling Type II formula because mutualistic interaction usually has a saturated response. Boundedness of solutions and nonexistence of periodic orbit are established. Global dynamics of the model demonstrate mechanisms by which mutualism can lead to coexistence/extinction of mutualists. In particular, intermediate mutualism is shown to be favorable under certain parameter ranges, but extremely strong/weak mutualism can result in extinction of one/both species. Saturation constant in the Holling Type II formula is exhibited to play a role in species coexistence. While seven novel types of dynamics of the model are displayed in a previous paper, analysis in this work confirms these types and presents a new one. Numerical simulations illustrate and extend our results.