A generic, hard transition to chaos

A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive values of a parameter F, no matter how small, a fully developed chaotic attractor exists within some domain of additional parameters, whereas no chaotic behavior exists for F < 0. As F is made positive, an unstable fixed point reaches an invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic structure existing at F = 0 make the limits t --* +oc, F ~ +0 non-commuting, and allow an exact description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators in near-resonance at any 2 : q frequency ratio, with F representing linear excitation of the first oscillator) is fully analysed

Experimental evidence of a hard transition to chaos

A generic, sudden transition to chaos has been experimentally verified using electronic circuits. The particular system studied involves the near resonance of two coupled oscillators at 2:1 frequency ratio when the damping of the first oscillator becomes negative. We identified in the experiment all types of orbits described by theory. We also found that a theoretical, ID limit map fits closely a map of the experimental attractor which, however, could be strongly disturbed by noise. In particular, we found noisy periodic orbits, in good agreement with noise theory.

Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Mapa preliminar de períodos predominantes del suelo en Puerto Príncipe (Haití) a partir de medidas de ruido ambiental.

The 2010 Haiti earthquake, occurred on January 12th at 16:53:09 local time (21:53:09 UTC) with epicentral distance of 15 km from the capital Port au Prince, MW 7.0 and 13 km hypocenter deep, was the strongest event in the area since happened in 1770. The maximum macroseismic intensity was estimated as X (MMI scale). The aim of this research is to obtain a preliminary zonation of Port-au-Prince in terms of predominant resonance periods of ground. A total of 36 short-period ambient noise records have been carried out on a grid of about 500x500m. H/V spectral ratio method (HVSR) has been applied to determine the predominant period at each point. The lowest values (<0.2s) predominate in the southern part of the city, composed by Miocene conglomerates, while highest values (> 0.45s) correspond to the center and western parts, composed of Pleistocene-Holocene alluvial deposits and anthropogenic land reclaimed from the sea. We have determined the ground VS30 structure inside National Palace garden, using simultaneous ambient noise measurements. An array made up of 6 sensors were used, with 5 of them uniformly distributed along a circumference and a sixth one placed in its centre. The records were analyzed by using the spatial autocorrelation method (SPAC). The VS 30 value obtained was 331m/sec, in good agreement with the average values obtained for this area by other authors, using prospecting techniques.