Humboldt-Universität zu Berlin - Mathematisch-Naturwissen­schaft­liche Fakultät - International Research Training Group 1740

Seminar Talk

Prof. Manuel Matias (IFISC Palma de Mallorca)

Title: Oscillatory and excitable dynamics of localized structures

Localized structures (LS) arise in a large variety of systems from a balance between nonlinearity and spatial coupling, and driving and dissipation. They have been suggested as bits in all-optical memories. A focus of our group in the last few years has been the characterization of a variety of dynamical regimes exhibited by these LS, like temporal oscillations and excitability. Here I will consider several examples of these studies. The first one is the characterization of the excitability behavior mediated by LS, that is different to the well known excitable media, as it is an emergent property of the system.
We have also studied the effect of noise on such excitable Type I behavior. The second one is the interaction of oscillatory LS, that are non punctual oscillators, and whose interaction through the interplay of coupling and the internal degrees of freedom, is not well understood. The third one is the interaction of LS in the excitable regime. We propose their use in computation, not just information storage, where bits are represented by an excitable excursion rather than by a stationary solution, and demonstrate the implementation of AND, OR and NOT optical gates, providing complete logic functionality. Finally, in many real systems LS are static, and so oscillatory instabilities and, thus, excitability are not generic. So, we discuss a completely general mechanism to induce such dynamical regimes, such as oscillations and excitable behavior, that relies on the interplay between spatial inhomogeneities and drift, and apply to a prototypical example of a gradient system that cannot exhibit oscillations: the 1-D Swift-Hohenberg equation.

D. Gomila, M.A. Matias and P. Colet, Phys. Rev. Lett. 94 063905 (2005). A. Jacobo, D. Gomila, M.A. Matias, and P. Colet, New J. Phys. 14 013040 (2012).
P. Parra-Rivas, D. Gomila, M.A. Matias, and P. Colet, Phys. Rev. Lett. 110 064103 (2013).