基于DDE-Biftool的时滞捕食-食饵收获模型的数值延拓与分歧分析
Numerical Continuation and Bifurcation Analysis in a Harvested Predator-Prey Model with Time Delay using DDE-Biftool
摘要：
时间延迟已被纳入模型，以反映某些物理或生物意义。延迟微分方程（DDEs）理论在近七十年来得到了广泛的发展，它可以用来研究时滞对系统动力学行为的影响。研究微分方程的数值工具不仅在说明理论结果方面，而且在发现模型的有趣动力学方面发挥了重要作用。DDE-Biftool是一个用于微分方程数值延拓和数值分岔分析的Matlab软件包，是目前最常用的微分方程数值分析工具之一。在本文中，我们提出了一个指南，使用最新版本的DDE-Biftool针对研究人员谁是新的时滞系统的研究。首先，我们将对一个具有单个离散时滞的捕食-被捕食模型的应用实例进行简短的讨论。然后，我们在DDE-Biftool中实现了这个示例模型，指出了初学者需要谨慎的功能。最后，我们的理论和数值结果的比较。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
