Feller, Chrystel Gabriel, Jean-Pierre Mazza, Christian Yerly, Florence 2014-03-01 The plant hormone auxin is fundamental for plant growth, and its spatial distribution in plant tissues is critical for plant morphogenesis. We consider a leading model of the polar auxin flux, and study in full detail the stability of the possible equilibrium configurations. We show that the critical states of the auxin transport process are composed of basic building blocks, which are isolated in a background of auxin depleted cells, and are not geometrically regular in general. The same model was considered recently through a continuous limit and a coupling to the von Karman equations, to model the interplay of biochemistry and mechanics during plant growth. Our conclusions might be of interest in this setting, since, for example, we establish the existence of Lyapunov functions for the auxin flux, proving in this way the convergence of pure transport processes toward the set of equilibrium points. application/pdf https://folia.unifr.ch/global/documents/303657 https://folia.unifr.ch/documents/303657/files/J._Math._Biol._2014_.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00285-013-0655-9 info:eu-repo/semantics/openAccess License undefined Journal of Mathematical Biology. - 2014, vol. 68, no. 4, p. 879–909 Auxin flux Pattern formation Reinforced random walks info:eu-repo/classification/udc/57 Pattern formation in auxin flux http://purl.org/coar/resource_type/c_6501