Asllani, MalborMalborAsllaniExpert, PaulPaulExpertCarletti, TimoteoTimoteoCarletti2018-09-262018-07-192018-09-262018-07-19PLoS Computational Biology, 2018, 14 (7)1553-734Xhttp://hdl.handle.net/10044/1/62694Many collective phenomena in Nature emerge from the -partial- synchronisation of the units comprising a system. In the case of the brain, this self-organised process allows groups of neurons to fire in highly intricate partially synchronised patterns and eventually lead to high level cognitive outputs and control over the human body. However, when the synchronisation patterns are altered and hypersynchronisation occurs, undesirable effects can occur. This is particularly striking and well documented in the case of epileptic seizures and tremors in neurodegenerative diseases such as Parkinson’s disease. In this paper, we propose an innovative, minimally invasive, control method that can effectively desynchronise misfiring brain regions and thus mitigate and even eliminate the symptoms of the diseases. The control strategy, grounded in the Hamiltonian control theory, is applied to ensembles of neurons modelled via the Kuramoto or the Stuart-Landau models and allows for heterogeneous coupling among the interacting unities. The theory has been complemented with dedicated numerical simulations performed using the small-world Newman-Watts network and the random Erdős-Rényi network. Finally the method has been compared with the gold-standard Proportional-Differential Feedback control technique. Our method is shown to achieve equivalent levels of desynchronisation using lesser control strength and/or fewer controllers, being thus minimally invasive.© 2018 Asllani et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Science & TechnologyLife Sciences & BiomedicineBiochemical Research MethodsMathematical & Computational BiologyBiochemistry & Molecular BiologyDEEP BRAIN-STIMULATIONCOUPLED OSCILLATORSPERTURBATION-THEORYPARKINSONS-DISEASEEPILEPSYMODELMECHANISMSNETWORKSCHAOSPOPULATIONSJournal Articlehttps://www.dx.doi.org/10.1371/journal.pcbi.1006296