具功能性反应的食饵—捕食者系统的定性研究

The Qualitative Study of a Prey-predator System with Functional Response

对一类具有HollingⅢ类功能性反应的食饵-捕食者系统进行了研究,主要讨论了系统平衡点的稳定性;并利用Dulac无环定理和发散量积分得到了系统无极限环的条件,最后利用张芷芬惟一性定理获得了极限环的存在惟一性定理.这些结果为进一步研究此类系统提供了可靠的理论依据.

A class of preypredator system with Holling Ⅲ functional response is studied. The stability of equilibrium is discussed mainly. The conditions of nonexistence of the limit cycle of system through Dulac's nocycle theorem and divergent integral are obtained. Finally, the theorem of the existence and uniqueness of the limit cycle of system are got through Zhang's uniqueness theorem of limit cycle. These results provide a reliable theoretical foundation for making further study this class of system.