Conditions for the Generation of Rhythms in a Discrete Dynamic System

To model phenotypic plasticity of plants in their environment, a new version of the functional-structural model GreenLab has been developed where a single variable representative of the plant sink and source balance controls different events in plant architecture, among which the numbers of fruits and of branches. Simulations revealed emergent properties of this model like the automatic generation of rhythms. Similar cyclic patterns in branch or fruit production may be observed in real plants. The model is based on the theory of discrete dynamic system. In this article, we present dynamic equations of the plant growth. It helps us explain rhythm generation and control the behaviour of the system. Conditions for the appearance of such rhythms are determined as functions of the plant endogenous parameters and the environmental conditions. It is at present a purely theoretical model but experiments are conducted to calibrate the model.