William Pasillas-Lépine

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Motivated by the recent development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of mean-field feedback and analyze the robustness of its phase-locking with respect to general inputs. Under standard assumptions, this system can be reduced to a modified version of the Kuramoto(More)
The aim of our paper is to provide a new class of five-phase anti-lock brake algorithms (that use wheel deceleration logic-based switching) and a simple mathematical background that explains their behavior. Firstly, we completely characterize the conditions required for our algorithm to work. Secondly, we explain how to compute analytically an approximation(More)
High-frequency deep brain stimulation is used to treat a wide range of brain disorders, like Parkinson's disease. The stimulated networks usually share common electrophysiological signatures, including hyperactivity and/or dysrhythmia. From a clinical perspective, HFS is expected to alleviate clinical signs without generating adverse effects. Here, we(More)
The model proposed by Wilson and Cowan (1972) describes the dynamics of two interacting subpopulations of excitatory and inhibitory neurons. It has been used to model neural structures like the olfactory bulb, whisker barrels, and the subthalamo-pallidal system. It is well-known that this system can exhibit an oscillatory behavior that is amplified by the(More)
In this paper we analyze the robustness of phaselocking in the Kuramoto system with arbitrary bidirectional interconnection topology. We show that the effects of timevarying natural frequencies encompass the heterogeneity in the ensemble of oscillators, the presence of exogenous disturbances, and the influence of unmodeled dynamics. The analysis, based on a(More)
Basal ganglia are interconnected deep brain structures involved in movement generation. Their betaband oscillations (13-30Hz) are known to be linked to Parkinson’s disease motor symptoms. In this paper, we provide conditions under which these oscillations may occur, by explicitly considering the role of the pedunculopontine nucleus (PPN). We analyze the(More)