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A theoretical framework is developed for a precise control of spatialpatterns in oscillatory media using nonlinear global feedback, where a properform of the feedback function corresponding to a specific pattern is predictedthrough the analysis of a phase diffusion equation with global coupling. Inparticular, feedback functions that generate the following spatial patterns areanalytically given: i) 2-cluster states with an arbitrary population ratio, ii)equally populated multi-cluster states, and iii) a desynchronized state. Ourmethod is demonstrated numerically by using the Brusselator model in theoscillatory regime. Experimental realization is also discussed.

Design principle of multi-cluster and desynchronized states in oscillatory media via nonlinear global feedback