带有Beddington-DeAngelis功能性反应函数的非自治捕食扩散时滞模型的研究(英文)  

Study on A Non-Autonomous Predator-Prey Dispersion-Delay Model with Beddington-DeAngelis Functional Response

作　　者：郑秀亮[1] 梦晓璐 高亚萍[1] 李博[1] 

机构地区：[1]河北北方学院理学院,张家口河北075000 [2]天津大学药物科学与技术学院,天津300072

出　　处：《生物数学学报》2014年第2期231-247,共17页Journal of Biomathematics

基　　金：Supported by the Scientific Research Foundation of Science and Technology Seismological Bureau of Zhang Jia Kou(12110034C-2);the Young Foundation of He Bei North University Natural Science Research Projects(Q201104)

摘　　要：研究了一类带有Beddington-DeAngelis功能性反应函数和食饵扩散的非自治变时滞捕食模型,首先运用微分方程中的比较原理证明了非自治系统的持久性,其次,当系统是周期系统时,通过构造合适的Lyapunov泛函,获得了周期系统具有唯一全局渐近稳定正周期解存在性的充分条件,最后通过数值举例验证了理论分析的可行性.In this paper,we consider a non-autonomous variable delays predatorprey model with Beddington-DeAngelis functional response and prey diffusion.First,by using comparison theorem of the differential equation,it is proved that the general non-autonomous system is permanent.Furthermore,if the system is a periodic one,by constructing a suitable Lyapunov functional,sufficient conditions which guarantee the existence,uniqueness and global asymptotic stability positive periodic solution of the system are obtained.Finally,a numerical example is carried out to support the theoretical analysis of the research.

关 键 词：捕食-食饵模型 BEDDINGTON-DEANGELIS功能性反应 扩散 全局渐近稳定性 变时滞 持久性 

分 类 号：O175[理学—数学]