Global dynamics of a predator-prey model

作者：Liu, Xiuxiang^*; Lou, Yijun

来源：Journal of Mathematical Analysis and Applications, 2010, 371(1): 323-340.

DOI：10.1016/j.jmaa.2010.05.037

• Predator-prey model
• Predator-dependent response
• Coexistence and extinction
• Complicated equilibrium
• Global stability
• Uniqueness of limit cycles

This paper deals with the dynamics of a predator-prey model with Hassell-Varley-Holling functional response. First, we show that the predator coexists with prey if and only if predator's growth ability is greater than its death rate. Second, using a blow-up technique, we prove that the origin equilibrium point is repelling and extinction of both predator and prey populations is impossible. Third, the local and global stability of the positive steady state coincide when the predator interference is large. Finally, for a typical biological case, we show instability of the positive equilibrium implies global stability of the limit cycle. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.

• 出版日期2010-11-1
• 单位华南师范大学