Plant behaviour: A mathematical approach for understandingintra-plant communication

Plants are far from being passive organisms being able to exhibit complex behaviours in response to environmental stimuli. How these stimuli are combined, triggered and managed is still an open and complex issue in biology. Mathematical models have helped in understanding some of the pieces in the complexity of intra-plant communication, but a larger and brighter view, setting together multiple key processes, is still missing. This paper proposes a fully coupled system of nonlinear, non-autonomous, discontinuous, ordinary differential equations to describe with accuracy the adapting behaviour and growth of a single plant, by deeply analysing the main stimuli affecting plant behaviour. The proposed model was developed, and here sustained, with the knowledge at the state of the art; and validated with a comparison among numerical results and a wide number of biological data collected from the literature, demonstrating its robustness and reliability. From the proposed analysis it is also shown an emerging self-optimisation of internal resources and feedback stimuli, without the need for defining an optimisation function for the wellness of the plant. The model is ultimately able to highlight the stimulus-signal of the intra-communication in plant, and it can be expanded and adopted as useful tool at the crossroads of disciplines as mathematics, robotics, biology, for instance for validation of biological hypothesis, translation of biological principles into control strategies or resolution of combinatorial problems.\n\nAuthor summaryPlants are able to adapt themselves to a wide range of conditions. The complexity and efficiency of this behaviour suggest a richness of signals exchanged that allowed scientists to talk about communication. Understanding this network of stimuli is an important challenge to increase biological knowledge as well as to adapt plant mechanisms to different research fields. To address this quest we developed a mathematical model able to describe what cues are fundamental in plant communication and how they interact each other.