Ageing of an oscillator due to frequency switching

If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs: (i) between two driving forces which have different frequencies, or (ii) as a single forcing whose frequency switches between two values. The difference is subtle, but entirely changes the long term behaviour, and concerns whether the switch can be expressed linearly or nonlinearly in terms of a discontinuous quantity (such as a sign or Heaviside step function that represents the switch between frequencies). In scenario (i) the oscillator has a stable periodic orbit, and the system can be described as a Filippov system. In scenario (ii) the oscillator exhibits hidden dynamics, which lies outside the theory of Filippov's systems, and causes the system to be increasingly (as time passes) dominated by sliding along the frequency-switching threshold, and in particular if periodic orbits do exist, they too exhibit sliding. We show that the behaviour persists, at least asymptotically, if the systems are regularized (i.e. if the switch is modelled as a smooth transition in the manner of (i) or (ii))

Novel slow-fast behaviour in an oscillator driven by a frequency-switching force

When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple periodically-forced harmonic oscillator, which disagree starkly in their predictions of its long time behaviour. Attempting to resolve the disagreement by `regularizing' the switch not only preserves the disagreement, but shows it increases with time. One of the models corresponds to a conventional `Filippov' description of a nonsmooth system, while the second exhibits a structure that irreversibly ages, developing a number of novel multi-scale behaviours that we believe have not been reported before. These include slow-fast staircases, novel mixed-mode oscillations, and a synchronized canard explosion. These features are proven to exist using asymptotic analysis, but as they involve a slow-fast time-scale separation that increases with time, they lie beyond the reach of numerical methods

Nuevos retos educativos ante el escenario de la universalización tecnológica : El caso de los estudios de comunicación

Los estudios de comunicación, especialmente en su vertiente de producción de comunicación audiovisual y multimedia, se mueven sobre las coordenadas representadas por: a) el contexto institucional universitario y su particular evolución en el caso español; b) los planes de estudio (las materias concretas) como materialización de toda una forma de entender la docencia en este campo; y c) el propio desarrollo y evolución del sector profesional (también con las particularidades del caso español). Estas tres coordenadas, evidentemente, son flexibles y dinámicas y tienen un denominador común: la presencia de las TIC (Tecnologías de la Información y la Comunicación) en mayor o menor grado, con mayor o menor influencia. La siguiente comunicación trata de establecer, de forma breve, los principales elementos de valoración a tener en cuenta ante el creciente fenómeno de la universalización tecnológica y de qué forma puede afectar (y, de hecho, ya afecta) la docencia universitaria y su relación con el sector profesional.Eje: Reflexiones educación Siglo XXIRed de Universidades con Carreras en Informática (RedUNCI