Cyclic data and planar ordinary differential equations: statistical modeling and inference

目前的计划是解决一个广泛的问题，这是估计ode（常微分方程）的解的参数出现在生物统计学应用中，并具有循环解。我们从生态学开始，重点是捕食者和猎物之间的相互作用；在实践中，许多动物种群表现出振荡行为。因此，在他们的模型中，生态学家正在考虑允许极限循环或螺旋达到平衡的系统。在我们的建议中，我们介绍了一种简单的方法来估计ODE系统的定性分析所提出的元素，如等斜线，例如，只要存在周期性，该方法就有效。一旦执行了估计，就可以测试各种模型。本方案的原创性是在相位平面上工作，方法是Froda & Colavita（2005）和Froda & Nkurunziza（2006）开发的方法的延伸。

The present program is on solving a broad question, which is to estimate parameters of solutions to ODEs (ordinary differential equations) that occur in biostatistical applications and have cyclic solutions. We start with ecology, and the emphasis is on predator-prey interactions; in practice, many animal populations exhibit oscillatory behaviour. Therefore, in their models, ecologists are considering systems that admit limit cycles or spiral to an equilibrium. In our proposal we introduce a simple method for estimating elements that are put forward by the qualitative analysis of the ODE system, like isoclines, e.g. The method works whenever periodicity is present. Once the estimation is performed, one can test various models as well. The originality of the present program is to work in the phase plane, and the methodology is an extension of the one developed in Froda & Colavita (2005) and Froda & Nkurunziza (2006).