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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)
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)
— In this paper we analyze the robustness of phase-locking in the Kuramoto system with arbitrary bidirectional interconnection topology. We show that the effects of time-varying natural frequencies encompass the heterogeneity in the ensemble of oscillators, the presence of exogenous disturbances, and the influence of unmodeled dynamics. The analysis, based(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)
— Basal ganglia are interconnected deep brain structures involved in movement generation. Their beta-band 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 pedun-culopontine nucleus (PPN). We analyze the(More)
We propose in this paper a constructive procedure that transforms locally, even at singular configurations, the kinematics of a car towing trailers into Kumpera-Ruiz normal form. This construction converts the nonholonomic motion planning problem into an algebraic problem (the resolution of a system of polynomial equations), which we illustrate by steering(More)
This paper shows that an active front steering control, that considers the nonlinear behaviour of the tire-road forces, can be designed by parameterizing the vehicle dynamics with respect to the measurable yaw rate and taking into account the steady state behaviour of the vehicle. In order to ensure the tracking of the yaw rate reference signal on the basis(More)