An elementary model of torus canards.

We study the recently observed phenomena of torus canards. These are a higher-dimensional generalization of the classical canard orbits familiar from planar systems and arise in fast-slow systems of ordinary differential equations in which the fast subsystem contains a saddle-node bifurcation of limit cycles. Torus canards are trajectories that pass near the saddle-node and subsequently spend long times near a repelling branch of slowly varying limit cycles. In this article, we carry out a study of torus canards in an elementary third-order system that consists of a rotated planar system of van der Pol type in which the rotational symmetry is broken by including a phase-dependent term in the slow component of the vector field. In the regime of fast rotation, the torus canards behave much like their planar counterparts. In the regime of slow rotation, the phase dependence creates rich torus canard dynamics and dynamics of mixed mode type. The results of this elementary model provide insight into the torus canards observed in a higher-dimensional neuroscience model.

[Comparison of the analgesic efficacy of EMLA 5% cream and lidocaine infiltration for biopsy of the genital mucosa]. / Comparison de l'efficacité analgésique d'EMLA 5 p. 100 crème et de l'infiltration de lidocaïne pour les biopsies des muqueuses génitales.

OBJECTIVE: To compare the analgesic efficacy of EMLA 5 p. 100 cream versus Xylocaïne 1 p. 100 infiltration for biopsies of the genital mucosa. PATIENTS AND METHODS: 63 adult patients were randomized. EMLA (0.3-5 g) was applied during 7-12 minutes, and Xylocaïne 1 p. 100 (0.2-5 ml) was infiltrated 0-10 minutes before biopsy. Pain during the anaesthetic procedure and the biopsy was assessed by the patient using a Visual Analogue Scale. RESULTS: Pain scores were significantly lower with EMLA application than Xylocaïne infiltration, but infiltration resulted in better surgical anaesthesia. The combined pain scores (anaesthetic procedure and biopsy) were lower in the EMLA group, but this difference failed to reach statistical significance. CONCLUSION: EMLA is a less painful anaesthetic procedure than infiltration, but has a lower analgesic efficacy. EMLA can be used as an alternative to infiltration for biopsies of the genital mucosa.