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In this article, we focus on a periodic resource allocation problem applied on a dynamical system which comes from a biological system. More precisely, we consider a system with 𝑁 resources and 𝑁 activities, each activity use the allocated resource to evolve up to a given time 𝑇 > 0 where a control (represented by a given permutation) will be applied on the system to reallocate the resources. T
