摘要
研究了一类具有恐惧因子和狩猎合作的捕食–食饵反应扩散模型,以此探讨恐惧因子和狩猎合作对捕食系统动力学性质的影响。通过分析正平衡点的特征方程,得到了平衡点的局部渐近稳定性。结果表明,若不考虑恐惧因子,以狩猎合作系数α作为分支参数,得到Hopf分支点α*。当合作系数大于α*时,将恐惧因子e作为分支参数,得到Hopf分支点e*,在Hopf分支点附近会产生空间齐次和非齐次的周期解。另外,讨论了由扩散引起Turing失稳的条件,结果表明,当捕食者与食饵扩散率之比较小时,系统存在空间非均匀稳态解。这些结论能为如何维持生态平衡提供理论依据,最后利用数值模拟验证所得结论。
A predator-prey reaction-diffusion model with a fear factor and hunting cooperative is studied to explore the effects of two factors on the behavior of the predator-prey system dynamics.The local asymptotic stability of the positive equilibrium point is analyzed by the characteristic equation of the positive equilibrium point.The Hopf bifurcation pointα∗is obtained by taking the hunting cooperation coefficientαas the bifurcation parameter without considering the fear factor.When the cooperation coefficient is greater than α*,the fear factor is used as the bifurcation parameter to obtain the Hopf bifurcation point e*,the spatially homogeneous and non-homogeneous periodic solutions are generated near the Hopf bifurcation point.In addition,the conditions of Turing instability caused by diffusion are discussed.The results show that the system has a spatially inhomogeneous steady state when the ratio of predator and prey diffusivity is small.These conclusions can provide theoretical basis for how to maintain ecological balance.Finally,the conclusions are verified by numerical simulation.
作者
陈清婉
柳文清
CHEN Qingwan;LIU Wenqing(College of General Education,Minnan Science and Technology Institute,Quanzhou 362300)
出处
《工程数学学报》
CSCD
北大核心
2023年第4期661-671,共11页
Chinese Journal of Engineering Mathematics
基金
福建省教育厅中青年教育科研项目(JAT210616
JAT200980)
福建省教育科学“十四五”规划课题(FJJKBK21-100)
泉州科技高层次人才创新创业项目(2018C094R).
