针对具有阶段结构、捕食者在妊娠期间含有时滞的分数阶生态流行病模型的稳定性进行研究。通过计算模型的特征根,运用Routh-Hurwitz判据,得到捕食者灭绝平衡点、无病平衡点和地方病平衡点的局部渐近稳定性;运用分数阶分岔理论,得到地方病平衡点附近产生Hopf分支的充分条件。同时研究发现,分数阶阶次对分岔点的影响,随着分数阶阶次的增加,模型的分岔点在减少。最后运用数值模拟验证理论结论的正确性。
In this paper, the stability of a fractional order ecological epidemic model with stage structure and predator delay time during pregnancy was studied. By calculating the characteristic roots of the model and using Routh-hurwitz criterion, it is obtained that the predator extinction equilibrium point, disease-free equilibrium point and endemic equilibrium point are locally asymptotically stability, a sufficient condition for the generation of Hopf bifurcation near the endemic equilibrium is obtained. At the same time, the influence of fractional order on the bifurcation point decreases is discussed, and it is found that the bifurcation point of the system decreases as the order increases. Finally, the validity of the theoretical conclusion is verified by numerical simulation.
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