庇护和收获效应对一类食饵-捕食模型的稳定性影响  

Influence of Refuge and Harvesting on the Stability of a Predator-Prey Model

作　　者：童姗姗[1] 牛玉俊[1] 窦霁虹[2] Tong Shanshan Niu Yujun Dou Jihong(School of Mathematics and Statistics, Nanyang Institute of Technology, Nanyang 473004, Henan China Department of Mathematics,Northwest University, Xi’an 710127, China)

机构地区：[1]南阳理工学院数学与统计学院,河南南阳473004 [2]西北大学数学系,西安710127

出　　处：《河南科学》2016年第10期1624-1629,共6页Henan Science

基　　金：国家自然科学基金资助项目(U1504105);南阳市软科学研究计划项目(2015RKX06);南阳理工学院教育教学改革研究资助项目(NIT2016SJJG-011)

摘　　要：研究了一类含庇护和收获效应的食饵-捕食模型.应用Hurwize判据、Dulac判据分析了系统平衡点局部稳定性、全局稳定性,并利用Pioncare-Bendixson环域定理得到了极限环唯一存在的充分条件.最终发现庇护和收获效应对此系统具有稳定化作用,调控庇护比例和收获强度可以将系统的正平衡点的由不稳定变成全局渐近稳定,从而实现食饵种群和捕食者种群的持久共存,为维持良好的生态平衡提供了一定理论依据.A prey-predator model with refuge and harvesting effect is discussed. By applying the Hurwize criterion and Dulac criterion,the local and global stability of equilibrium points of the system are analyzed,the existence and uniqueness of limit cycle are obtained by using the Pioncare-Bendixson ring region theorem. Eventually,the stabilizing effect of refuge and harvesting is obtained,the regulation of asylum ratio and harvest intensity can be positive equilibrium point of the system is not stable into global asymptotic stability ,thus achieving lasting coexistence of prey and predator,and the model provides a certain theoretical basis to maintain a good ecological balance.

关 键 词：庇护所 平衡点 极限环 

分 类 号：O175.1[理学—数学]