ZHANG Jiehua,WANG Qingjuan.Almost periodic solutions of a discrete competitive system with Beddington - DeAngelis functional response[J].Journal of Yanbian University,2021,47(02):105-110.
一类具有Beddington - DeAngelis功能反应的离散竞争系统的概周期解
- Title:
- Almost periodic solutions of a discrete competitive system with Beddington - DeAngelis functional response
- 文章编号:
- 1004-4353(2021)02-0105-06
- 分类号:
- O175.14
- 文献标志码:
- A
- 摘要:
- 针对一类具有Beddington - DeAngelis功能反应的离散竞争系统,运用差分不等式和通过构造适当的Lyapunov函数,证明了该系统具有持久性和全局吸引性.利用差分概周期方程的壳理论,得到了保证该系统存在唯一的概周期解的充分条件.所得结果补充了文献[3]和文献[4]的工作.
- Abstract:
- A class of discrete competition system with Beddington - DeAngelis functional response is studied in this paper. By applying the difference inequality theory and constructing the suitable Lyapunov functional, we show that the system is permanent and globally attractive. Further, by using almost periodic functional hull theory, sufficient conditions which guarantee the existence of a unique global attractive positive almost periodic sequence solution of the system. The results supplement the literature [3] and [4].
参考文献/References:
[1] BEDDINGTON J R. Mutual interference between parasites or predators and its effect on searching efficiency[J]. J Animal Ecodogy, 1975,44(1):331-340.
[2] DEANGELIS D L, GOLDSTEIN R A, O'NEILL R V. A model for tropic interaction[J]. Ecology, 1975,56:881-892.
[3] YU S, CHEN F. Dynamic behaviors of a competitive system with Beddington -DeAngelis functional response[J]. Discrete Dyn Nat Soc, 2019:1-12. Article ID 4592054.
[4] ZHANG J, YU S, WANG Q. Extinction and stability of a discrete competitive system with Beddington -DeAngelis functional response[J]. Engineering Letters, 2020,28(2):406-411.
[5] CHEN F, CHEN X, HUANG S. Extinction of a two species non -autonomous competitive system with Beddington- DeAngelis functional response and the effect of toxic substances[J]. Open Math, 2016,14:1157-1173.
[6] XIAO Z, LI Z, ZHU Z, et al. Hopf bifurcation and stability in a Beddington -DeAngelis predator -prey model with stage structure for predator and time delay incorporating prey refuge[J]. Open Math, 2019,17:141-159.
[7] CHEN B. Global attractivity of a Holling -Tanner model with Beddington -DeAngelis functional response: with or without prey refuge[J]. Engineering Letters, 2019,27(4):1-9.
[8] 张杰华.具时滞和反馈控制的离散互惠系统的概周期解[J].延边大学学报(自然科学版),2016,42(2):108-114.
[9] ZHANG S N. Existence of almost periodic solution for difference systems[J]. Ann Differ Equ, 2000,16(2):184-206.
[10] LI Z, CHEN F D, HE M X. Almost periodic solutions of a discrete Lotka -Volterra competition system with delays[J]. Nonlinear Anal Real World Appl, 2011,12(4):2344-2355.
[11] FINK A M, SEIFERT G. Liapunov functions and almost periodic solutions for almost periodic systems[J]. J Differential Equations, 1969,5:307-313.
[12] YUAN R, HONG J L. The existence of almost periodic solutions for a class of differential equations with piecewise constant argument[J]. Nonlinear Anal, 1997,28(8):1439-1450.
[13] CHEN F D. Permanence for the discrete mutualism model with time delays[J]. Math Comput Model, 2008,47:431-435.
备注/Memo
收稿日期: 2021-02-23基金项目: 福建省教育厅中青年教师教育科研项目(JAT190976,JAT190975)
作者简介: 张杰华(1983—),女,副教授,研究方向为生物数学.