Dynamical and Statistical Criticality in a Model of Neural Tissue

For the nervous system to work at all, a delicate balance of excitation and inhibition must be achieved. However, when such a balance is sought by global strategies, only few modes remain balanced close to instability, and all other modes are strongly stable. Here we present a simple model of neural tissue in which this balance is sought locally by neurons following `anti-Hebbian' behavior: {\sl all} degrees of freedom achieve a close balance of excitation and inhibition and become "critical" in the dynamical sense. At long timescales, the modes of our model oscillate around the instability line, so an extremely complex "breakout" dynamics ensues in which different modes of the system oscillate between prominence and extinction. We show the system develops various anomalous statistical behaviours and hence becomes self-organized critical in the statistical sense

Universality in Three-Frequency Resonances

We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems

Burridge-Knopoff Models as Elastic Excitable Media

We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global oscillations, period-doubled pacemakers, and propagating fronts. We suggest that examples of elastic excitable media are to be found in such diverse physical systems as Burridge-Knopoff models of frictional sliding, electronic transmission lines, and active optical waveguides

Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon.Comment: 10 pages including 12 postscript figures, revtex. Additional work in http://www.imedea.uib.es/Nonlinear . The paper with higher-resolution figures can be obtained from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

Population dynamics advected by chaotic flows: a discrete-time map approach

A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map possibly yielding Lagrangian chaos. Each {\it fluid particle} carries concentrations of active substances which evolve according to its own reaction dynamics. This evolution is also modeled in terms of maps. Motivated by the question, of relevance in marine ecology, of how a localized distribution of nutrients or preys affects the spatial structure of predators transported by a fluid flow, we study a specific model in which the population dynamics is given by a logistic map with space-dependent coefficient, and advection is given by the standard map. Fractal and random patterns in the Eulerian spatial concentration of predators are obtained under different conditions. Exploiting the analogies of this coupled-map (advection plus reaction) system with a random map, some features of these patterns are discussed.Comment: 22 pages, 5 figure

Excitability and optical pulse generation in semiconductor lasers driven by resonant tunneling diode photo-detectors

We demonstrate, experimentally and theoretically, excitable nanosecond optical pulses in optoelectronic integrated circuits operating at telecommunication wavelengths (1550 nm) comprising a nanoscale double barrier quantum well resonant tunneling diode (RTD) photo-detector driving a laser diode (LD). When perturbed either electrically or optically by an input signal above a certain threshold, the optoelectronic circuit generates short electrical and optical excitable pulses mimicking the spiking behavior of biological neurons. Interestingly, the asymmetric nonlinear characteristic of the RTD-LD allows for two different regimes where one obtain either single pulses or a burst of multiple pulses. The high-speed excitable response capabilities are promising for neurally inspired information applications in photonics. (C) 2013 Optical Society of AmericaFCT [PTDC/EEA-TEL/100755/2008]; FCT Portugal [SFRH/BPD/84466/2012]; Ramon y Cajal fellowship; project RANGER [TEC2012-38864-C03-01]; Direcci General de Recerca del Govern de les Illes Balears; EU FEDER funds; Ministry of Economics and Competitivity of Spain [FIS2010-22322-C02-01