Plykin-like attractor in non-autonomous coupled oscillators

A system of two coupled non-autonomous oscillators is considered. Dynamics of complex amplitudes is governed by differential equations with periodic piecewise continuous dependence of the coefficients on time. The Poincar\'{e} map is derived explicitly. With exclusion of the overall phase, on which the evolution of other variables does not depend, the Poincar\'{e} map is reduced to 3D mapping. It possesses an attractor of Plykin type located on an invariant sphere. Computer verification of the cone criterion confirms the hyperbolic nature of the attractor in the 3D map. Some results of numerical studies of the dynamics for the coupled oscillators are presented, including the attractor portraits, Lyapunov exponents, and the power spectral density.Comment: 11 pages, 9 figure

First cases of Omicron in France are exhibiting mild symptoms, November 2021–January 2022

International audienceObjectivesWe aimed to investigate the first Omicron cases detected in France in order to assess case characteristics and provide supporting information on the possible impact of this variant on the healthcare system.MethodsA standardized questionnaire was used to collect information from confirmed and probable Omicron cases.ResultsMedian age of 468 investigated cases was 35 years, 376 were symptomatic (89%); 64% were vaccinated with two doses and 7% had received three doses. Loss of smell and taste were reported by 8.3% and 9% of cases, respectively. Seven cases were hospitalized, three of those were unvaccinated (including two with reported precondition). No admissions to intensive care and no deaths were reported.ConclusionsOur results confirm a mild clinical presentation among the first Omicron cases detected in France and highlight the importance for the national COVID-19 surveillance system to quickly detect and adapt to the emergence of a new variant