Dynamic analysis of a fractional order delayed predator-prey system with harvesting
Dynamic analysis of a fractional order delayed predator-prey system with harvesting
复制标题
带有收获的分数阶延迟捕食者-被捕食系统的动态分析
DOI：
10.1007/s12064-016-0223-0
复制
发表时间：
2016
影响因子：
1.1
通讯作者：
Zhang Xuebing
中科院分区：
文献类型：
--
作者：
Song Ping;Zhao Hongyong;Zhang Xuebing
在这项研究中，我们考虑了带有收获条件的分数阶延迟捕食者-被捕食者系统。我们的讨论分为两种情况。在没有收获的情况下，我们研究模型的稳定性，并通过分析相关的特征方程得出一些标准。通过收获，我们从局部稳定性的角度研究系统的动态，并分析收获对猎物和捕食者的影响。最后，提出数值模拟来验证我们的理论结果。此外，通过数值模拟，我们研究了分数阶和收获项对动态行为的影响。我们的数值结果表明，分数阶不仅会影响系统在没有收获项的情况下的稳定性，还会影响从稳定到不稳定以及再到稳定的切换时间。收获可以转换平衡点、稳定性和稳定性切换时间。
In the study, we consider a fractional order delayed predator–prey system with harvesting terms. Our discussion is divided into two cases. Without harvesting, we investigate the stability of the model, as well as deriving some criteria by analyzing the associated characteristic equation. With harvesting, we investigate the dynamics of the system from the aspect of local stability and analyze the influence of harvesting to prey and predator. Finally, numerical simulations are presented to verify our theoretical results. In addition, using numerical simulations, we investigate the effects of fractional order and harvesting terms on dynamic behavior. Our numerical results show that fractional order can affect not only the stability of the system without harvesting terms, but also the switching times from stability to instability and to stability. The harvesting can convert the equilibrium point, the stability and the stability switching times.