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. 2022 May 10;10(1):coac026. doi: 10.1093/conphys/coac026

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© The Author(s) 2022. Published by Oxford University Press and the Society for Experimental Biology.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fast dynamics of the root–shoot model, implemented with additional state variables for the shared surplus of nitrogen and carbon, and . Biomass of root and shoot is kept constant. In the full system (with changing biomasses), this phase plane would change as the slow state variables evolve. The phase plane shown here reveals bistability of the fast dynamics. The system has three equilibria. The two outer (stable) equilibria correspond to states where is high and where is high (the other surplus sharing rate being zero). The equilibria characterize states where only the root growing and only the shoot growing. The two basins of attraction are separated by an unstable equilibrium and a separatrix. Brighter colors for the vectors indicate stronger attraction. Parameters: , , , , , and . Root and shoot biomass are fixed: and .

Inline graphic — Fast dynamics of the root–shoot model, implemented with additional state variables for the shared surplus of nitrogen and carbon, and . Biomass of root and shoot is kept constant. In the full system (with changing biomasses), this phase plane would change as the slow state variables evolve. The phase plane shown here reveals bistability of the fast dynamics. The system has three equilibria. The two outer (stable) equilibria correspond to states where is high and where is high (the other surplus sharing rate being zero). The equilibria characterize states where only the root growing and only the shoot growing. The two basins of attraction are separated by an unstable equilibrium and a separatrix. Brighter colors for the vectors indicate stronger attraction. Parameters: , , , , , and . Root and shoot biomass are fixed: and .