摘要
研究了一类食饵具有竞争者的捕食-食饵模型的稳定性问题,模型中考虑了恐惧因子和捕食者的消化时滞,建立了一个时滞微分方程模型。对模型的非负性,有界性,平衡点的全局稳定性和Hopf分支进行了数学分析。通过数值模拟,验证了模型理论的正确性,分析了时滞和其他生物参数(如恐惧因子、食饵的转化率)的作用。结果表明:较高水平的恐惧可以稳定系统,而相对低水平的恐惧会破坏系统的稳定性;当食饵转化率/消化时滞较大时,系统出现周期振荡,当食饵转化率/消化时滞较小时系统趋于稳定。
The stability of a predator-prey model with competitors and fear effect was studied.This model incorporated fear effect and the time delay which accounts for the gestation period of the predator,and a delay differential equation model was established.The non-negativity,boundedness of the model,global stability of the equilibrium point and Hopf branch were mathematically analyzed.Through numerical simulations,the correctness of the theoretical results were verified and the effects of time delay and other biological parameters(such as fear factor,conversion rate of prey)were explored.The results show that a higher level of fear can stabilize the system,while a relatively low level of fear will destroy the stability of the system.When the conversion rate of prey/gestation delay is big,the system appears periodic oscillations,and when the conversion rate of prey/gestation delay is small,the system tends to be stable.
作者
刘白茹
刘俊利
吕潘
LIU Bairu;LIU Junli;LYU Pan(School of Science,Xi′an Polytechnic University,Xi′an 710600,China)
出处
《沈阳大学学报（自然科学版）》
CAS
2022年第2期153-163,共11页
Journal of Shenyang University：Natural Science
基金
国家自然科学基金资助项目(11801431)
陕西省自然科学基础研究计划项目(2021JM-445)
陕西省青年杰出人才项目(10701000506)
西安工程大学研究生创新基金资助项目(chx2021033)。
