摘要
考虑一类带有恐惧效应和Allee效应的捕食者-食饵模型,研究2种效应对生物种群的影响。讨论了非负平衡点的存在性,并通过Lyapunov函数、Bendixson-Dulac定理分析非负平衡点局部及全局稳定性;给出Hopf分支的存在条件;利用数值模拟反映恐惧因子k和Allee常数m、n对种群动力学的影响。结果表明:增加恐惧效应或Allee效应会使种群(捕食者)的数量有所减少,且Allee常数m比常数n更明显地反映种群数量的变化。
A predator-prey model with fear effect and Allee effect is considered,and the influence of two effects on biological population is studied.The existence condition of non-negative equilibrium points is discussed,and the local and global stability of non-negative equilibrium points are analyzed by Lyapunov function and Bendixson-Dulac theorem.The existence condition of Hopf bifurcation is given.The influence of fear factor k and Allee constants m and n on the population dynamics is reflected by numerical simulation.The results show that increasing the fear effect or Allee effect will reduce the number of predators,and Allee constant m reflects the change of population more obviously than constant n.
作者
王欢
邢慧
WANG Huan;XING Hui(School of Science, Xi’an Polytechnic University, Xi’an 710048,China)
出处
《纺织高校基础科学学报》
CAS
2020年第4期85-90,共6页
Basic Sciences Journal of Textile Universities
基金
国家自然科学基金数学天元基金(11626182)
西安工程大学博士科研启动基金(BS1433)。
