Slowly oscillating periodic solutions for the Nicholson's blowflies equation with state‐dependent delay
Slowly oscillating periodic solutions for the Nicholson's blowflies equation with state‐dependent delay
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DOI：
10.1002/mma.4388
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发表时间：
2017-09
影响因子：
2.9
通讯作者：
Ling Zhang;Shangjiang Guo
中科院分区：
文献类型：
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作者：
Ling Zhang;Shangjiang Guo
在本文中，我们研究了具有状态相关延迟的尼克尔森苍蝇方程的动力学。对于恒定延迟，已知随着延迟的增加，在正平衡处会出现一系列 Hopf 分岔，并且周期解的全局存在性已成立。在这里，我们考虑状态相关延迟而不是恒定延迟，并将结果推广到在参数和延迟函数的一组温和条件下存在缓慢振荡周期解的结果。特别是，当正平衡变得不稳定时，全局不稳定流形将正平衡连接到缓慢振荡的周期轨道。版权所有 © 2017 约翰威利父子有限公司
In this paper, we study the dynamics of a Nicholson's blowflies equation with state‐dependent delay. For the constant delay, it is known that a sequence of Hopf bifurcation occurs at the positive equilibrium as the delay increases and global existence of periodic solutions has been established. Here, we consider the state‐dependent delay instead of the constant delay and generalize the results on the existence of slowly oscillating periodic solutions under a set of mild conditions on the parameters and the delay function. In particular, when the positive equilibrium gets unstable, a global unstable manifold connects the positive equilibrium to a slowly oscillating periodic orbit. Copyright © 2017 John Wiley & Sons, Ltd.