Deep brain stimulation (DBS) entails the delivery of a stimulation signal to subcortical structures via implanted electrodes. DBS has received a lot of attention as a therapeutic procedure in various neurological and neuropsychiatric disorders 
. DBS of different targets in the basal ganglia-thalamocortical loop is used to treat symptoms of Parkinson’s disease (PD) and other motor disorders 
; e.g. the subthalamic nucleus (STN) is a standard anatomical target for DBS in PD.
The hypokinetic symptoms of PD have been related to excessive beta-band oscillations and synchrony in the basal ganglia and other structures 
. Thus DBS effectiveness has been linked to the destruction of this pathological rhythmicity by reducing the bursting, oscillations and synchronization in the beta-band and increasing regularity and synchrony in the high-frequency band 
However, standard DBS, while clinically effective, does not completely restore motor function and has substantial side effects, which may be related to its strong stimuli and “one size fits all” approach. Standard DBS is associated with a variety of adverse effects such as dyskinesia, paraesthesia, dysarthria and gait disturbances 
. Non-motor adverse effects (mania, impulsivity, depression, various cognitive alterations, suicidal behavior, etc.) are also a problem 
. They can arise due to current spread to adjacent structures and due to the fact that associative, limbic and motor circuits, although traditionally viewed as largely parallel in the basal ganglia, are not completely independent 
These considerations lead to a strong interest in new DBS algorithms. Ideally, stimulation waveforms should have small amplitudes and should be targeted specifically to destruction of the pathological activity which results in the primary symptoms. Low amplitudes of stimulation will also save battery life, reducing the need for battery-replacement surgeries.
One method which has received a lot of attention recently and has appeared to be very promising is delayed feedback. This elegant feedback control scheme rendered the synchronized state in an ensemble of all-to-all coupled oscillators unstable 
. In the limit of a large number of oscillators, the amplitude of feedback signals vanishes, which makes it especially attractive. This control scheme was modified into a more realistic setting by using delayed feedback based on a mean field signal (a proxy for easy-to-record local field potentials, LFP) in order to cancel the effect of coupling and desynchronize ensembles of coupled oscillators 
. Subsequent studies provided further computational evidence for the ability of delayed feedback to destabilize a synchronized state (e.g., 
Therefore, the delayed feedback desynchronization algorithm appears to be quite robust. However, in spite of these advances and in spite of hardware availability 
, to our knowledge, this strategy has never been implemented in patients. There may be many reasons why the considered desynchronization technique has resisted effective clinical realization. The goal of this paper is to explore the action of delayed feedback DBS in a realistically partially-synchronous network. We conjecture that a complex origin of partially synchronous neural dynamics in parkinsonian brain may be a substantial obstacle to the implementation of delayed feedback desynchronization.
To study this problem, we employ a computational model of the basal ganglia network which successfully reproduces experimentally recorded neural activity 
. The synchronous activity in the PD brain is very intermittent 
. The model in 
is based on the membrane properties of the basal ganglia cells and is tuned in such a way as to reproduce not only the average synchrony levels, but also the temporal patterns of the synchronous dynamics seen in human experimental data. In the language of dynamical systems theory, this model realistically describes the dynamics not only in the vicinity of the synchronized state, but also in other parts of the phase space, ensuring more similarity between the model and the experimental system 
. In contrast, earlier studies used neural oscillators in a fully synchronized regime.
We will investigate the action of delayed stimulation as we vary network parameters to go from completely synchronized dynamics to more realistic intermittent synchrony. As a result we can see how delayed feedback DBS is performing in a setting whose dynamics is more faithful to that seen in PD patients.