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Article consultable en ligne : https://www.nature.com/articles/s41598-017-14773-3; International audience; Rapid progress in the area of humanoid robots offers tremendous possibilities for investigating and improving social competences in people with social deficits, but remains yet unexplored in schizophrenia. In this study, we examined the influence of social feedbacks elicited by a humanoid robot on motor coordination during a human-robot interaction. Twenty-two schizophrenia patients and twenty-two matched healthy controls underwent a collaborative motor synchrony task with the iCub humanoid robot. Results revealed that positive social feedback had a facilitatory effect on motor coordination in the control participants compared to non-social positive feedback. This facilitatory effect was not present in schizophrenia patients, whose social-motor coordination was similarly impaired in social and non-social feedback conditions. Furthermore, patients’ cognitive flexibility impairment and antipsychotic dosing were negatively correlated with patients’ ability to synchronize hand movements with iCub. Overall, our findings reveal that patients have marked difficulties to exploit facial social cues elicited by a humanoid robot to modulate their motor coordination during human-robot interaction, partly accounted for by cognitive deficits and medication. This study opens new perspectives for comprehension of social deficits in this mental disorder.

We show that a planar slow–fast piecewise-linear (PWL) system with three zones admits limit cycles that share a lot of similarity with van der Pol canards, in particular an explosive growth. Using phase-space compactification, we show that these quasi-canard cycles are strongly related to a bifurcation at infinity. Furthermore, we investigate a limiting case in which we show the existence of a continuum of canard homoclinic connections that coexist for a single-parameter value and with amplitude ranging from an order of ε to an order of 1, a phenomenon truly associated with the non-smooth character of this system and which we call super-explosion .

The well-studied Hindmarsh-Rose model of neural action potential is revisited from the point of view of global bifurcation analysis. This slow-fast system of three paremeterised differential equations is arguably the simplest reduction of Hodgkin-Huxley models capable of exhibiting all qualitatively important distinct kinds of spiking and bursting behaviour. First, keeping the singular perturbation parameter fixed, a comprehensive two-parameter bifurcation diagram is computed by brute force. Of particular concern is the parameter regime where lobe-shaped regions of irregular bursting undergo a transition to stripe-shaped regions of periodic bursting. The boundary of each stripe represents a fold bifurcation that causes a smooth spike-adding transition where the number of spikes in each burst is increased by one. Next, numerical continuation studies reveal that the global structure is organised by various curves of homoclinic bifurcations. In particular the lobe to stripe transition is organised by a sequence of codimension-two orbit- and inclination-flip points that occur along {\em each} homoclinic branch. Each branch undergoes a sharp turning point and hence approximately has a double-cover of the same curve in parameter space. The sharp turn is explained in terms of the interaction between a two-dimensional unstable manifold and a one-dimensional slow manifold in the singular limit. Finally, a new local analysis is undertaken using approximate Poincar\'{e} maps to show that the turning point on each homoclinic branch in turn induces an inclination flip that gives birth to the fold curve that organises the spike-adding transition. Implications of this mechanism for explaining spike-adding behaviour in other excitable systems are discussed., Comment: 32 pages, 18 figures, submitted to SIAM Journal on Applied Dynamical Systems