Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction–Diffusion Systems in $${\mathbb {R}}^2$$R2

@article{Iron2014LogarithmicEA,
  title={Logarithmic Expansions and the Stability of Periodic Patterns of Localized Spots for Reaction–Diffusion Systems in \$\$\{\mathbb \{R\}\}^2\$\$R2},
  author={David Iron and John Rumsey and Michael J. Ward and Juncheng Wei},
  journal={Journal of Nonlinear Science},
  year={2014},
  volume={24},
  pages={857-912}
}
The linear stability of steady-state periodic patterns of localized spots in $${\mathbb {R}}^2$$R2 for the two-component Gierer–Meinhardt (GM) and Schnakenberg reaction–diffusion models is analyzed in the semi-strong interaction limit corresponding to an asymptotically small diffusion coefficient $${\displaystyle \varepsilon }^2$$ε2 of the activator concentration. In the limit $${\displaystyle \varepsilon }\rightarrow 0$$ε→0, localized spots in the activator are centered at the lattice points… CONTINUE READING

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