Control of extreme events in the bubbling onset of wave turbulence.

We show the existence of an intermittent transition from temporal chaos to turbulence in a spatially extended dynamical system, namely, the forced and damped one-dimensional nonlinear Schrödinger equation. For some values of the forcing parameter, the system dynamics intermittently switches between ordered states and turbulent states, which may be seen as extreme events in some contexts. In a Fourier phase space, the intermittency takes place due to the loss of transversal stability of unstable periodic orbits embedded in a low-dimensional subspace. We mapped these transversely unstable regions and perturbed the system in order to significantly reduce the occurrence of extreme events of turbulence.

Spatial recurrence analysis: a sensitive and fast detection tool in digital mammography.

Efficient diagnostics of breast cancer requires fast digital mammographic image processing. Many breast lesions, both benign and malignant, are barely visible to the untrained eye and requires accurate and reliable methods of image processing. We propose a new method of digital mammographic image analysis that meets both needs. It uses the concept of spatial recurrence as the basis of a spatial recurrence quantification analysis, which is the spatial extension of the well-known time recurrence analysis. The recurrence-based quantifiers are able to evidence breast lesions in a way as good as the best standard image processing methods available, but with a better control over the spurious fragments in the image.

Two-state on-off intermittency caused by unstable dimension variability in periodically forced drift waves.

Certain high-dimensional dynamical systems present two or more attractors characterized by different energy branches. For some parameter values the dynamics oscillates between these two branches in a seemingly random fashion, a phenomenon called two-state on-off intermittency. In this work we show that the dynamical mechanism underlying this intermittency involves the severe breakdown of hyperbolicity of the attractors through a mechanism known as unstable dimension variability. We characterize the parametric evolution of this variability using statistical properties of the finite-time Lyapunov exponents. As a model system that exhibits this behavior we consider periodically forced and damped drift waves. In this spatiotemporal example there is a low-dimensional chaotic attractor that is created by an interior crisis, already presenting unstable dimension variability.

Two-state on-off intermittency and the onset of turbulence in a spatiotemporally chaotic system.

We show the existence of two-state on-off intermittent behavior in spatially extended dynamical systems, using as an example the damped and forced drift wave equation. The two states are stationary solutions corresponding to different wave energies. In the language of (Fourier-mode) phase space these states are embedded in two invariant manifolds that become transversely unstable in the regime where two-state on-off intermittency sets in. The distribution of laminar duration sizes is compatible with the similar phenomenon occurring in time only in the presence of noise. In an extended system the noisy effect is provided by the spatial modes excited by the perturbation. We show that this intermittency is a precursor of the onset of strong turbulence in the system.