Cloud–rain predator–prey interactions: Analyzing some propertiesof the Koren–Feingold model and introduction of a new species-competition bulk system with a Hopf bifurcation

Abstract

This paper deals with some properties of predator–prey cloud–rain models. Focus is put on scaling and on some mathematical features such as stability and limit cycles. Precisely, the Koren–Feingold delay differential equation model is first investigated and it is shown that it has no limit cycles. Then, by considering another point of view (i.e. species competition dynamics) for parametrizing cloud–rain processes, a system of ordinary differential equations to model these processes is formulated. Some examples are given to illustrate that this model reproduces in a realistic way the essential macroscopic behavior of a cloud–rain system. The model has a Hopf bifurcation at which certain properties of cloud–rain interactions in the model are represented. This is an important point to prepare for further examination of cloud synchronization in a cloud field by Kuramoto model, for instance.