论文标题
使用DDE-Biftool的时间延迟，在收获的捕食者捕集模型中的数值延续和分叉分析
Numerical Continuation and Bifurcation Analysis in a Harvested Predator-Prey Model with Time Delay using DDE-Biftool
论文作者
论文摘要
时间延迟已被纳入模型，以反映某些物理或生物学含义。在过去的七十年左右的时间里，延迟微分方程（DDE）的延迟微分方程理论可用于检查所考虑的系统动力学行为的时间延迟的影响。研究DDE的数值工具不仅在说明理论结果，而且在发现模型的有趣动态方面发挥了重要作用。 DDE-Biftool是用于DDE的数值延续和数值分叉分析的MATLAB软件包，是DDE的最受使用和流行的数值工具之一。在本文中，我们介绍了使用最新版本的DDE-Biftool指南，该DDE-Biftool针对的是对时间延迟系统研究的研究人员。将首先介绍对具有单个离散时间延迟的收获捕食者捕集模型的示例应用程序的简短讨论。然后，我们在DDE-Biftool中实现此示例模型，指出了初学者需要谨慎的功能。我们以理论和数值结果的比较结尾。
Time delay has been incorporated in models to reflect certain physical or biological meaning. The theory of delay differential equations (DDEs), which has seen extensive growth in the last seventy years or so, can be used to examine the effects of time delay in the dynamical behavior of systems being considered. Numerical tools to study DDEs have played a significant role not only in illustrating theoretical results but also in discovering interesting dynamics of the model. DDE-Biftool, which is a Matlab package for numerical continuation and numerical bifurcation analysis of DDEs, is one of the most utilized and popular numerical tools for DDEs. In this paper, we present a guide to using the latest version of DDE-Biftool targeted to researchers who are new to the study of time delay systems. A short discussion of an example application, which is a harvested predator-prey model with a single discrete time delay, will be presented first. We then implement this example model in DDE-Biftool, pointing out features where beginners need to be cautious. We end with a comparison of our theoretical and numerical results.
