Feedback stabilization of non-uniform spatial pattern in reaction-diffusion systems

In this paper, we formulate and solve feedback stabilization problem of unstable non-uniform spatial pattern in reaction-diffusion systems. By considering spatial spectrum dynamics, we obtain a finite dimensional approximation that takes over the semi-passivity of the original partial differential equation. By virtue of this property, we can show the diffusive coupling in the spatial frequency domain achieves the desired pattern formation.

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