论文标题
在空间异质环境中，扩散尼科尔森的吹蝇模型的稳定性和霍普夫分叉
The stability and Hopf bifurcation of the diffusive Nicholson's blowflies model in spatially heterogeneous environment
论文作者
论文摘要
在本文中，当扩散速率较大时，我们考虑了在空间异质环境中的扩散尼科尔森的吹风模型。我们表明，人均鸡蛋产量的平均生产率与死亡率的平均比率会影响模型的动力学。如果比率小于临界值，则独特的正稳态在局部渐近稳定。但是，当比率大于临界值时，较大的时间延迟可以通过HOPF分叉使独特的正稳态不稳定。尤其是，当扩散速率趋于无穷大时，第一个HOPF分叉值趋向于“平均” DDE模型。此外，我们表明，HOPF分叉的方向是向前的，并且第一个HOPF分叉值的分叉周期性解决方案是轨道渐近稳定的，这改善了WEI和LI（非线性肛门，60：1351-1367，2005）的较早结果。
In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the death rate affects the dynamics of the model. The unique positive steady state is locally asymptotically stable if the ratio is less than a critical value. However, when the ratio is greater than the critical value, large time delay can make the unique positive steady state unstable through Hopf bifurcation. Especially, the first Hopf bifurcation value tends to that of the ''average'' DDE model when the diffusion rate tends to infinity. Moreover, we show that the direction of the Hopf bifurcation is forward, and the bifurcating periodic solution from the first Hopf bifurcation value is orbitally asymptotically stable, which improves the earlier result by Wei and Li (Nonlinear. Anal., 60: 1351-1367, 2005).
