具有Holling Ⅱ型功能性捕食函数的时滞扩散云杉蚜虫模型的Hopf分支  

Hopf Bifurcation in a Delayed Diffusive Spruce Budworm Model with Holling Ⅱ Predation Function

作　　者：汤小松[1] 王志伟[1] TANG XIAOSONG;WANG ZHIWEI(School of Mathematics and Physics,Jinggangshan University,Ji'an 343009,China)

机构地区：[1]井冈山大学数理学院,吉安343009

出　　处：《应用数学学报》2024年第5期833-844,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:11761038);江西省教育厅科技项目(批准号:GJJ2201612,GJJ211027);江西省自然科学基金(批准号:20212BAB202021)资助项目。

摘　　要：为探究云杉蚜虫周期性爆发的影响因素,本文在纽曼边值条件下提出了一类具有Holling Ⅱ型功能性捕食函数的时滞扩散云杉蚜虫模型.众所周知,自然界中种群的演化不仅依赖现在的状态,而且还依赖过去的状态.这意味着,考虑时滞能更好地反映生态系统中的某些现象.为此,以时滞为参数,利用特征方程和分析技巧研究了该模型正平衡点的稳定性和单个时滞、两个时滞分别诱发Hopf分支的存在性问题.最后,通过数值模拟,获得了该模型稳定的周期解,这为云杉蚜虫的周期性爆发原因提供了理论指依据.此外,结果表明两个时滞诱发Hopf分支发生的时滞临界值要比单个时滞情形要小.For the aim of exploring the influencing factors of periodic outbreaks of spruce budworm,we proposed a delayed diffusive spruce budworm model with Holling Ⅱ predation function under the homogeneous Neumann boundary condition.As is known to all,the evolution of many populations is relate with not only the present situation,but also with the past situation.This implies that it is essential to take over the effect of delay on reflecting the phenomena.For this aim,choosing the delay as bifurcating parameter,we investigated the stability of the positive equilibrium and the existence of Hopf bifurcation deduced by single delay or two delays by using the characteristic equation and mathematical analysis skills.Finally,through performing numerical simulations,we obtained the stable periodic solutions of this model,which provided the theoretical basis for periodic outbreaks of spruce budworm.Moreover,the numerical results indicated that the critical value of Hopf bifurcation deduced by two delays is smaller than one of Hopf bifurcation deduced by single delay.

关 键 词：云杉蚜虫模型 扩散 双时滞 HOPF分支 周期解 

分 类 号：O175.1[理学—数学]