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

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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).