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**\(2^n\)-splitting or edge-splitting? A manner of splitting in dissipative systems.**
*(English)*
Zbl 0983.35061

The splitting of pulses in reaction-diffusion systems, especially for the Gray-Scott model, is investigated. In experiments and numerical calculations it has been observed that self-replicating patterns are produced by splitting of the pulses at the boundary, leading to the creation of 2 new pulses in every step for the one-dimensional case. In this paper the transient dynamics is investigated by reducing the system to a local invariant manifold close to the bifurcation point and investigating the resulting ODE. Starting from a single pulse it is shown that in this model only the pulses at the boundary split.

Reviewer: Alois Steindl (Wien)

### MSC:

35K57 | Reaction-diffusion equations |

35B32 | Bifurcations in context of PDEs |

35B40 | Asymptotic behavior of solutions to PDEs |

35B42 | Inertial manifolds |

### Keywords:

self-replicating pattern; pulse solution; Turing patterm; wave splitting; saddle-node bifurcation; Gray-Scott model
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\textit{S.-i. Ei} et al., Japan J. Ind. Appl. Math. 18, No. 2, 181--205 (2001; Zbl 0983.35061)

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### References:

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