Fenómenos oscilatorios lineales y no lineales en sistemas dinámicos discretos y continuos

Esta tesis presenta los resultados originales obtenidos a lo largo de un estudio unificado de problemas oscilatorios de distinto número de grados de libertad, con énfasis en los fenómenos auto-oscilatorios y de sincronzación. Se incluyen casos de baja dimensión y de dimensión infinita presentando el material en orden creciente de complejidad.Facultad de Ciencias Exacta

Fenómenos oscilatorios lineales y no lineales en sistemas dinámicos discretos y continuos

Esta tesis presenta los resultados originales obtenidos a lo largo de un estudio unificado de problemas oscilatorios de distinto número de grados de libertad, con énfasis en los fenómenos auto-oscilatorios y de sincronzación. Se incluyen casos de baja dimensión y de dimensión infinita presentando el material en orden creciente de complejidad.Facultad de Ciencias Exacta

Síntesis e implementación en FPGA de un mapa caótico con PDF Gaussiana

Los generadores de Ruido Blanco Gaussiano AWGN (Additive White Gaussian Noise) constituyen un insumo básico para la medición de los sistemas de comunicaciones digitales. En la actualidad existen varios métodos de generación de AWGN que parten de secuencias aleatorias con PDF (Probability Density Function) uniforme y requieren implementar en hardware operaciones complejas. En este trabajo se diseña e implementa en hardware un generador de ruido gaussiano basado en un mapa caótico. La ventaja radica en el hecho de que los sistemas caóticos deterministas son descriptos por ecuaciones alineales simples, y por lo tanto son sencillos de implementar en hardware. Para lograr que la secuencia generada presente la PDF deseada se sintetiza el mapa caótico, que será el corazón del sistema, mediante un método basado en la teoría de las matrices positivas. La calidad de las secuencias generadas es evaluada mediante cuantificadores de aleatoriedad. La implementación en hardware se realiza en una FPGA Cyclone III EP3C120F780C7, empleando la placa de desarrollo 3C120 Development Board de ALTERA.Sección: Diseño de hardware FPGACentro de Técnicas Analógico-Digitale

Quantifiers for randomness of chaotic pseudo random number generators

We deal with randomness quantifiers and concentrate on their ability to discern the hallmark of chaos in time series used in connection with pseudo-random number generators (PRNGs). Workers in the field are motivated to use chaotic maps for generating PRNGs because of the simplicity of their implementation. Although there exist very efficient general-purpose benchmarks for testing PRNGs, we feel that the analysis provided here sheds additional didactic light on the importance of the main statistical characteristics of a chaotic map, namely (i) its invariant measure and (ii) the mixing constant. This is of help in answering two questions that arise in applications: (i) which is the best PRNG among the available ones? and (ii) if a given PRNG turns out not to be good enough and a randomization procedure must still be applied to it, which is the best applicable randomization procedure? Our answer provides a comparative analysis of several quantifiers advanced in the extant literature.Instituto de Física La Plat

Distinguishing noise from chaos

Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.Instituto de Física La Plat

Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approach

By recourse to appropriate information theory quantifiers (normalized Shannon entropy and Martin-Plastino-Rosso intensive statistical complexity measure), we revisit the characterization of Gaussian self-similar stochastic processes from a Bandt-Pompe viewpoint. We show that the ensuing approach exhibits considerable advantages with respect to other treatments. In particular, clear quantifiers gaps are found in the transition between the continuous processes and their associated noises.Centro de Investigaciones ÓpticasInstituto de Física La PlataFacultad de Ingenierí

Causality and the Entropy-Complexity Plane: Robustness and Missing Ordinal Patterns

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the "causal" entropy-complexity plane [Rosso et al. Phys. Rev. Lett. 99 (2007) 154102] and ii) the estimation of the decay rate of missing ordinal patterns [Amig\'o et al. Europhys. Lett. 79 (2007) 50001, and Carpi et al. Physica A 389 (2010) 2020-2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r = 4) to which we added correlated noise (colored noise with f-k Power Spectrum, 0 {\leq} k {\leq} 2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy-complexity plane this goal can be achieved without additional computations.Comment: submitted to Physica