Abstract
A theoretical framework is developed for the precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the analysis of a phase diffusion equation with global coupling. In particular, feedback functions that generate the following spatial patterns are analytically given: (i) 2-cluster states with an arbitrary population ratio, (ii) equally populated multi-cluster states and (iii) a desynchronized state. Our method is demonstrated numerically by using the Brusselator model in the oscillatory regime. Experimental realization is also discussed.
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