A一类三种群时滞捕食系统模型A Class of Three-species Predator-prey System with Time Delay
马仁雪,谢伟杰,李佳倩,江月
摘要(Abstract)：
研究了一类三种群时滞捕食系统模型的稳定性.以食饵种群的消极负反馈时滞为分支参数,利用特征值方法,得到系统模型局部渐近稳定的充分条件并确定了模型产生Hopf分支的时滞临界点.最后,利用数值模拟验证了所得结果正确性.
关键词(KeyWords)： 时滞捕食系统;种群;稳定性;Hopf分支
基金项目(Foundation): 2016年度安徽省自然科学基金青年项目(1608085QF151)
作者(Author): 马仁雪,谢伟杰,李佳倩,江月
DOI: 10.16393/j.cnki.37-1436/z.2016.05.007
参考文献(References)：
- [1]T.K.Kar,A.Batabyal.Persistence and stability of a two prey one predator system[J].International Journal of Engineering,Science and Technology,2010,2(2):174-190.
- [2]徐昌进.时标上具有阶段结构的三种群捕食系统的周期解[J].经济数学,2013,30(1):5-11.
- [3]A.Farajzadeh,M.H.Rahmani Doust,F.Haghighifar,D.Baleanu.The stability of gauss model having one-prey and two-predators[J].Abstract and Applied Analysis,2012,1(1):1-9.
- [4]Cui Guo-hu,Yan Xiang-ping.Stability and bifurcation analysis on a three-species food chain system with two delays[J],Communications in Nonlinear Science and Numerical Simulation,2011,16(9):3704-3720.
- [5]Meng Xin-you,Huo Hai-feng,Zhang Xiao-bing,Xiang Hong.Stability and Hopf bifurcation in a three-species system with feedback delays[J].Donlinear Dynamics,2011,64(4):349-364.
- [6]Meng Xin-you,Huo Hai-feng,Zhang Xiao-bing.Stability and global Hopf bifurcation in a delayed food web consisting of aprey and two predators[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(9):4335-4348.
- [7]刘娟.一类时滞竞争捕食系统模型的Hopf分支[J].滨州学院学报,2015,31(4):32-35.
- [8]B.D.Hassard,N.D.Kazarinoff,Y.H.Wan,Theory and Applications of Hopf Bifurcation[M].Cambridge University Press,Cambridge,1981.