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

A theoretical framework is developed for a 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.