[1]李畅通,冯孝周.一类具有B-D功能反应项的捕食系统的定性分析[J].西安工业大学学报,2020,(01):1-8.[doi:10.16185/j.jxatu.edu.cn.2020.01.001 ]
 LI Changtong,FENG Xiaozhou.Qualitative Analysis of the Predator-Prey Model with B-D Functional Response[J].Journal of Xi'an Technological University,2020,(01):1-8.[doi:10.16185/j.jxatu.edu.cn.2020.01.001 ]
点击复制

一类具有B-D功能反应项的捕食系统的定性分析()
分享到:

《西安工业大学学报》[ISSN:1673-9965/CN:61-1458/N]

卷:
期数:
2020年01期
页码:
1-8
栏目:
基础科学
出版日期:
2020-02-15

文章信息/Info

Title:
Qualitative Analysis of the Predator-Prey Model with B-D Functional Response
文章编号:
1673-9965(2020)01-0001-08
作者:
李畅通冯孝周
(西安工业大学 理学院,西安 710021
Author(s):
LI ChangtongFENG Xiaozhou
(School of Science,Xi'an Technological University,Xi'an 710021,China)
关键词:
周期解 持续生存 脉冲 混沌
Keywords:
periodic solution permanence impulse chaos
分类号:
O175.14
DOI:
10.16185/j.jxatu.edu.cn.2020.01.001
文献标志码:
A
摘要:
为了解决害虫防防治策略因农业资源有限引起的非线性影响,文中对具有非线性脉冲控制的捕食系统进行了定性分析.利用脉冲微分方程中的Floquet理论,证明了当脉冲周期小于某临界值时,系统的害虫根除周期解是局部渐近稳定的,并利用分支理论得到非平凡周期解的存在性的条件.数值上验证了具有非线性脉冲的系统有非常丰富的动力学性质.
Abstract:
Pest control strategies are inevitably affected by limited agricultural resources, in order to simulate the nonlinear effect since the resource limitation.The predator-prey system with B-D functional response is proposed and analyzed.It is proved that there exists a local stable pest-free periodic solution when impulsive period is less than a certain critical value.The existence of nontrivial periodic solution is established on the bifurcation theory.The numerical results show that the system with limited resource has complex dynamical behavior.

参考文献/References:

[1] LIU B,ZHANG Y J,CHEN L S.The Dynamical Behaviors of a Lotka-Volterra Predator-Prey Model Concerning Integrated Pest Management[J].Nonlinear Anal:Real World Applications,2005,6(2):227. [2] TANG S Y,XIAO Y N,CHEKE R A.Multiple Attractors of Host-parasitoid Models with Integrated Pest Management Strategies:Eradication,Persistence and Outbreak[J].Theoretical Population Biology,2008,73(2):181. [3] GAO W,TANG S Y.The Effects of Impulsive Releasing Methods of Natural Enemies on Pest Control and Dynamical Complexity[J].Nonlinear Analysis:Hybrid Systems,2011,5(3):540. [4] XIANG Z Y,SONG X Y.The Dynamical Behaviors of a Food Chain Model with Impulsive Effect and Ivlev Functional Response[J].Chaos Solitons & Fractals,2009,39(15):2282. [5] TANG S Y,TANG G Y,CHEKE R A.Optimum Timing for Integrated Pest Management:Modeling Rates of Pesticide Application and Natural Enemy Releases[J].Journal of Theoretical Biology,2010,264(2):623. [6] LI C T,TANG S Y.The Effects of Timing of Pulse Spraying and Releasing Periods on Dynamics of Generalized Predator-Prey model[J].International Journal of Biomathematics,2012,5(1):1. [7] TANG S Y,LIANG J H.Global Qualitative Analysis of a Non-Smooth Gause Predator-Prey Model with a Refuge[J].Nonlinear Analysis,2013,76(1):165. [8] WANG S,HUANG Q D.Bifurcation of Nontrivial Periodic Solutions for a Beddington-De Angelis Interference Model with Impulsive Biological Control[J].Applied Mathematical Modelling,2014,39:1470. [9] BAKE H K.Qualitative Analysis of Beddington-DeAngelis Type Impulsive Predator-Prey Models[J].Nonlinear Anal:Real World Applications,2010,11:1312. [10] YANG J,TANG S Y.Holling Type II Predator-Prey Model with Nonlinear Pulse as State-Dependent Feedback Control[J].Journal of Computational and Applied Mathematics,2016,291(1):225. [11] TIAN Y,TANG S Y,CHEKE R A.Dynamic Complexity of a Predator-Prey Model for IPM with Nonlinear Impulsive Control Incorporating a Regulatory Factor for Predator Releases[J].Mathematical Modelling and Analysis,2019,24(1):134. [12] LI C T,TANG S Y.Analyzing a Generalized Pest-Natural Enemy Model with Nonlinear Impulsive Control[J].Open Mathematics,2018,16(1):1390. [13] LAKMECHE A,ARINO O.Bifurcation of Non-Trivial Periodic Solutions of Impulsive Differential Equations Arising Chemotherapeutic Treatment[J].Dynamics of Continuous,Discrete and Impulsive Systems,2000,7(2):265.

相似文献/References:

[1]李畅通,戴 飞,冯孝周.具有脉冲控制的Ivlev型捕食系统<[J].西安工业大学学报,2012,(01):5.
 LI Changtong,DAI Fei,FENG X.Dynamic Behavior of Pluse Cont[J].Journal of Xi'an Technological University,2012,(01):5.

备注/Memo

备注/Memo:
收稿日期:2019-09-07
基金资助:国家自然科学基金(61772017; 61102144); 陕西省教育厅专项科研计划资助项目(18JK0393); 西安工业大学研究生教改项目(2017033)。 第一
作者简介:李畅通(1982-),男,西安工业大学讲师,主要研究方向为生物数学,E-mail:lctnihao@163.com。
(编辑、校对 肖 晨)
更新日期/Last Update: 2020-02-15