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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.

MSC:

35K57 Reaction-diffusion equations
35B32 Bifurcations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B42 Inertial manifolds

Software:

HomCont; AUTO
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References:

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