一类具有时滞的捕食者-猎物-共生者系统的研究

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 1001-1013.

一类具有时滞的捕食者-猎物-共生者系统的研究

郑立飞¹(),郭洁¹,吴美华²,王小瑞¹,万阿英^2,*

¹ 西北农林科技大学理学院陕西杨凌 712100
² 呼伦贝尔学院数学与统计学院内蒙古呼伦贝尔 021008

收稿日期:2017-03-08 出版日期:2018-10-26 发布日期:2018-11-09
通讯作者: 万阿英 E-mail:zhenglifei@nwsuaf.edu.cn
作者简介:郑立飞, E-mail: zhenglifei@nwsuaf.edu.cn
基金资助:
国家自然科学基金(11461024);呼伦贝尔市科技局项目(9110/KY0156);西北农林科技大学基本科研业务费专项资金(2014YB023);西北农林科技大学基本科研业务费专项资金(2452015086);西北农林科技大学基本科研业务费专项资金(z109021561);陕西省扶持学科数学学科基金(14SXZD007)

The Research on a Class of the Predator-Prey-Mutualist System with Delays

Lifei Zheng¹(),Jie Guo¹,Meihua Wu²,Xiaorui Wang¹,Aying Wan^2,*

¹ College of Science, Northwest A F University, Shaan'xi Yangling 712100
² College of Mathematics and Statistics, Hulunbuir Univeristy, Inner Mongolia Hailar 021008

Received:2017-03-08 Online:2018-10-26 Published:2018-11-09
Contact: Aying Wan E-mail:zhenglifei@nwsuaf.edu.cn
Supported by:
the NSFC(11461024);the Science and Technology Bureau's Project of Hulunbeier City(9110/KY0156);the National Higher-Education Institution General Research and Development Project(2014YB023);the National Higher-Education Institution General Research and Development Project(2452015086);the National Higher-Education Institution General Research and Development Project(z109021561);the Supportive Subject Foundation of Shaanxi Province(14SXZD007)

摘要/Abstract

摘要：

该文建立了具有时滞的捕食者-猎物-共生者系统模型，对模型的正性，持久性和局部稳定性记性了分析.得出此系统具有稳定的可能，正平衡点也具有渐近稳定的可能.最后用棉蚜生态系统中的瓢虫、棉蚜、蚂蚁的相关数据进行数值模拟，得出猎物和捕食者的发育历期（时滞）对整个系统具有重要影响，若发育历期过长，则整个系统将具有周期性的波动.

关键词: 时滞, 捕食者-猎物-共生者系统, 局部稳定性, 数值模拟

Abstract:

In this paper, we establish a predator-prey-mutualist system with time delay, and the positive, persistence and local stability of the system are analyzed. The conclusion shows that it is possible that the system is stable, and the positive equilibrium point is asymptotically stable. Finally, numerical simulation with the relevant data in the ecosystem of ladybirds, cotton aphids and ants.The results show that development duration (time delay) of the prey and predator has an important influence on the whole system, and if growth duration is too long, the whole system will have periodic fluctuations.

Key words: Time Delay, Predator-prey-mutualist, Local Stability, Numerical modeling

中图分类号:

O175

郑立飞,郭洁,吴美华,王小瑞,万阿英. 一类具有时滞的捕食者-猎物-共生者系统的研究[J]. 数学物理学报, 2018, 38(5): 1001-1013.

Lifei Zheng,Jie Guo,Meihua Wu,Xiaorui Wang,Aying Wan. The Research on a Class of the Predator-Prey-Mutualist System with Delays[J]. Acta mathematica scientia,Series A, 2018, 38(5): 1001-1013.

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