文档介绍：东北师范大学硕士学位论文带有食饵避难的Leslie-Gower捕食者—食饵扩散系统的定性分析姓名:单尧申请学位级别:硕士专业:应用数学指导教师:王静 20090401 摘要本文主要是研究带有食饵避难的Leslie-Gower捕食者一食饵扩散系统,并对其进行定性分析. 全文共分五章,()的非负常稳态的弥散性、持久性及稳定性,本章得出所讨论系统在当参数满足 a2bl>alr2(1一m)2成立时具有持久性;、,在特殊参数范围内,,通过比较发现:食饵的避难保护只对吸引域的大小有影响,但并不能影响系统的稳定性. 关键词:;Lyapunov函数;扩散;食饵避难 Abstract Thispaper is tostudyqualitativeproperties ofsolutions totheLeslie—Gower predator-prey diffusionsystem withtheprey refuge. The full textisdivided firstchapter outlinesthe thesecond chapter,we firststudy thedissipation,persistence and stability ofnon—negative constant steady states ofsystem(),If theassumption a2bl>air2(1一m)2 holds,thesystem ispersistent;Then,by constructing asuit· able Lyapunov function,we show thattwo non·negative constant steady states ofthesystem alegloballyasymptotically stablefor certainranges oftheparam- HI,a priori upper and lower bounds forpositivesteady statesof thesystem are IV,the nonexistence ofnonconstant positive steady statesofthesystem forcertainranges V paring the results between thesystem withtheprey refuge and norefuge,we show thattheprey refuge couldinfluence thesizeofthe attractiondomain,but it has no influence onthestability ofthe system. Keywords:Leslie-Gower;Lyapunov function;Diffusion;Prey refuge Ⅱ独创性声明本人郑重声明:,除了特别加以标注和致谢的地方外,,. 学位论文作者签名,晕趣 Ii 冱2f:!!?。/ 学位论文使用授权书本学位论文作者完全了解东北师范大学有关保留、使用学位论文的规定,即:东北师范大学有权保留并向国家有关部门或机构送交学位论文的复印件和电子版,,可以采用影印、缩印或其它复制手段保存、汇编本学位论文. (保密的学位论文在解密后适用本授权书) 学位论文作者签名:墅指导教师签名。之歪; 日期:坐!I:!;.01 期:礁哇。皇篓:of 学位论文作者毕业后去向: 工作单位: 通讯地址: 电话:——邮编:——东北师范大学硕士学位论文第一章引言在生物数学中,,