论文标题
离散平面图的增强相平面方法：介绍下一题操作员
An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators
论文作者
论文摘要
介绍了与平面离散图的无效相关的下一介质运算符和相应的下一介质根系和根曲线。描述了如何通过包括与其nullclines相关的根手术器的符号来增强包括无效和方向场的标准相肖像，从而产生增强的相肖像。与nullcline关联的下一介质操作员的符号确定一个点是在相应的nullcline上方还是下方映射的，例如，可以识别积极的不变区域。使用Lotka-Volterra类型竞争模型，我们演示了如何构建增强相肖像。我们表明，增强阶段肖像提供了一种基本的，替代方法来确定该模型的完整全局动态。我们通过考虑一个涉及互助的模型和捕食者捕集模型来进一步探索增强相肖像的局限性和潜力。
The next-iterate operators and corresponding next-iterate root-sets and root-curves associated with the nullclines of a planar discrete map are introduced. How to augment standard phase portraits that include the nullclines and the direction field, by including the signs of the root-operators associated with their nullclines, thus producing an augmented phase portrait, is described. The sign of a next-iterate operator associated with a nullcline determines whether a point is mapped above or below the corresponding nullcline and can, for example, identify positively invariant regions. Using a Lotka-Volterra type competition model, we demonstrate how to construct the augmented phase portrait. We show that the augmented phase portrait provides an elementary, alternative approach for determining the complete global dynamics of this model. We further explore the limitations and potential of the augmented phase portrait by considering a Ricker competition model, a model involving mutualism, and a predator-prey model.
