Bifurcations of equilibria in a mathematical model for metal growth

Deborah Lacitignola

Abstract


In this paper we focus on a morphochemical reaction-diffusion model for metal growth whose capability to support spatial patterns was essentially associated to the diffusion-driven instability of a specific system equilibrium, the equilibrium Pe. However, this model exhibits a rich multiplicity of other equilibria. We show that several bifurcations involving some of the many equilibria of the DIB modelcan affect the system spatial-organization properties by allowing for the existence of a subregion inside the Pe's Turing parameter space where the system trajectories can also tend towards a spatially homogeneous equilibrium and the existence of a region outside the Pe's Turing parameter space where spatial patterns can emerge.

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DOI: http://dx.doi.org/10.1478/AAPP.96S3A10

Copyright (c) 2018 Deborah Lacitignola

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This work is licensed under a Creative Commons Attribution 4.0 International License.