Fig 1. A schematic description of the control strategy.

An array of neuronal patches (white circles) is controlled using M = 2 microelectrodes (red-blue cones). The signals, KRsin(Ψ − ϕ_i), i = 1, 2, acquired by each microelectrode are passed (red arrows) to the controller that computes the control signals, $S_i^{stim}({\varphi }_1,{\varphi }_2)$, i = 1, 2, which are in turn (blue arrows) injected back to the neuronal patches 1 and 2. This determines an electromagnetic field which possesses a spatial extension whose strength decays with the distance from the injection point (large circles with shaded of blue). In this way nearby neuronal patches are also influenced but in a weaker fashion. The mechanism is presented as a sequence of steps repeated cyclically (external grey circular arrows), however under the assumption that the measurement and the computation of the control and the injection are very fast with respect to the natural time scale of the underlying system, this process can be considered to be instantaneous and thus acting directly on the evolution of the system without any delay (see Eq (14)).