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 bifurca- tions involving some of the many equilibria of the DIB model can 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 spa- tially homogeneous equilibrium and the existence of a region outside the Pe’s Turing parameter space where spatial patterns can emerge.
Bifurcation of equilibria in a mathematical model for metal growth
Lacitignola,D.
2018-01-01
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 bifurca- tions involving some of the many equilibria of the DIB model can 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 spa- tially homogeneous equilibrium and the existence of a region outside the Pe’s Turing parameter space where spatial patterns can emerge.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
