具有时滞及Beddington-DeAngelis功能反应的食物链系统周期解的存在性与全局渐近稳定性  

EXISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTION IN A FOOD-CHAIN SYSTEM WITH DELAYS AND BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE

作　　者：熊友兵[1] 李红智[2] 

机构地区：[1]天津工业大学理学院,天津300160 [2]河北农业大学理学院,保定071001

出　　处：《系统科学与数学》2008年第3期288-301,共14页Journal of Systems Science and Mathematical Sciences

摘　　要：研究了具有时滞和Beddington-DeAngelis功能反应的一类食物链系统,通过运用Mawhin重合度理论中的延拓定理,得到了系统至少存在一个周期解的充分条件,并通过构造Lyapunov泛函的方法得到了系统周期解的全局稳定性.A delayed three-species food-chain model with Beddington-DeAngelis functional response is investigated. By using Gaines and Mawhin＇s continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions to the proposed model. By constructing a suitable Lyapunov functional, the global asymptotic stability of the periodic solutions is established.

关 键 词：时滞 功能反应 周期解 重合度 全局稳定性 

分 类 号：O175[理学—数学] Q141[理学—基础数学]