### Abstract

Original language | English |
---|---|

Pages (from-to) | 1948-1969 |

Number of pages | 22 |

Journal | COMPUTERS & MATHEMATICS WITH APPLICATIONS |

Volume | 70 |

Publication status | Published - 2015 |

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### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*COMPUTERS & MATHEMATICS WITH APPLICATIONS*,

*70*, 1948-1969.

**Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth.** / Gambino, Gaetana; Lupo, Salvatore; Sammartino, Marco Maria Luigi; Lacitignola; Sgura; Bozzini.

Research output: Contribution to journal › Article

*COMPUTERS & MATHEMATICS WITH APPLICATIONS*, vol. 70, pp. 1948-1969.

}

TY - JOUR

T1 - Weakly nonlinear analysis of Turing patterns in a morphochemical model for metal growth

AU - Gambino, Gaetana

AU - Lupo, Salvatore

AU - Sammartino, Marco Maria Luigi

AU - Lacitignola, null

AU - Sgura, null

AU - Bozzini, null

PY - 2015

Y1 - 2015

N2 - We 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.

AB - We 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.

KW - Bifurcation analysis

KW - Computational Mathematics

KW - Computational Theory and Mathematics

KW - Modeling and Simulation

KW - Morphochemical electrodeposition

KW - Pattern formation

KW - Reaction-diffusion

KW - Turing instability

UR - http://hdl.handle.net/10447/162170

M3 - Article

VL - 70

SP - 1948

EP - 1969

JO - COMPUTERS & MATHEMATICS WITH APPLICATIONS

JF - COMPUTERS & MATHEMATICS WITH APPLICATIONS

SN - 0898-1221

ER -