We suggest a scheme of a two-component synthetic gene network with competitive dynamics and study its model. The whole network comprises two parts which are separated between cell populations and mutually suppress each other's activity. Bistability is shown to exist for a lumped model describing local dynamics. For a distributed model, which describes spatio-temporal dynamics of a mixture of both populations, we have shown the existence of either static fronts in the case of symmetry between the competiting parts or propagating fronts in the case of asymmetry.
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