ODE (Ordinary Differential Equation) Models for Plant Circadian Networks: What the Models Are and How They Should Be...

ODE models have been used for decades to help circadian biologists understand the rhythmic phenomena they observe and to predict the behavior of plant circadian rhythms under changed conditions such as genetic mutations or novel environments. The models vary in complexity, and for good reasons, but they share the same mathematical ingredients in their construction and the same computational methods in their solution. Here we explain the fundamental concepts which define ODE models. We sketch how ODE models can be understood, how they can be solved mathematically and computationally, and the important distinction between autonomous and non-autonomous phenomena. The concepts are illustrated with examples which illustrate the basic concepts and which may help to describe the strengths and limitations of these models and the computational investigations of their properties.