Dynamic behaviors of a commensal symbiosis model with non-monotonic functional response and non-selective harvesting in a partial closure

A two species commensal symbiosis model with non-monotonic functional response and non-selective harvesting in a partial closure takes the form /dt&=&x(a₁-b₁x+₁y /d₁+y²)-q₁Emx, /dt&=&y(a₂-b₂y)-q₂Emy is proposed and studied, where aᵢ, bᵢ, qᵢ, i=1,2 c₁, E, $m(0<m<1)$ and d₁ are all positive constants. Depending on the range of the parameter m, the system may be collapse, or partial survival, or the two species could be coexist in a stable state. We also show that if the system admits a unique positive equilibrium, then it is globally asymptotically stable. By introducing the harvesting term and the reserve area, the system exhibit rich dynamic behaviors. Our results generalize the main results of Chen and Wu (A commensal symbiosis model with non-monotonic functional response, Commun. Math. Biol. Neurosci. 2017 (2017), Article ID 5).