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Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth
No full textWe focus on the morphochemical reaction–diffusion model introduced in Bozzini et al.
(2013) and carry out a nonlinear bifurcation analysis with the aim to characterize the shape
and the amplitude of the patterns arising as the result of Turing instability of the physically
relevant equilibrium. We perform a weakly nonlinear multiple scales analysis, and derive
the normal form equations governing the amplitude of the patterns. These amplitude equations
allow us to construct relevant solutions of the model equations and reveal the presence
of multiple branches of stable solutions arising as the result of subcritical bifurcations.
Hysteretic type phenomena are highlighted also through numerical simulations. We show
the occurrence of spatial pattern propagation and derive the Ginzburg–Landau equation
describing the envelope of the traveling wavefront
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