Extending a 1D Multi-Scale Plant Growth Model to Include Branching under Environmental and Soil Nutrient Dynamics

In this work, we extend the 1D multi-scale hybrid model of plant growth introduced by Bessonov and Volpert, which describes plant elongation driven by nutrient uptake from the soil but does not account for environmental effects such as temperature and solar radiation on growth or branching. We aim to generalize this framework to describe plant development under dynamic environmental conditions and soil nutrients while allowing the emergence of lateral branches. To this end, we build on the branching mechanism regulated by the interacting dynamics of auxin and cytokinin in the Bessonov-Volpert model, and we introduce environmental influence through an effective time variable based on Effective Day Degrees, which integrates temperature and solar radiation. This modification leads to a growth velocity that is no longer constant, as originally assumed in the Bessonov Volpert model, but depends explicitly on environmental fluctuations. The resulting model couples local hormonal signaling with nutrient-dependent growth and environmentally driven constraints. Numerical simulations illustrate how variations in soil nutrient availability and environmental conditions shape branching patterns and overall plant architecture. This extended formulation provides a mathematically consistent and biologically grounded framework for analyzing adaptive plant growth in dynamic environments.