Influence of an exogenous model parameter on the steady states in an auxin transport model

Abstract

Transport models of growth hormones contain many different parameters that determine the behavior of the system. Understanding the influence of these parameters will allow us to predict the patterns that emerge in the models when the parameters are changed and is therefore an important research topic. This paper studies the influence of an exogenous model parameter in the auxin transport model of Smith et al. [1] for a one-dimensional row of uniform square cells. The occurrence of different auxin patterns in function of the flux at the boundaries is observed by using numerical continuation methods and bifurcation analysis. For certain exogenous parameter ranges, we identified a s-shaped bistable bifurcation scenario. We found that the auxin pattern can change instantly if the auxin flux at the boundaries exceeds a certain threshold.