Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy

The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit highdimensional chaotic fluctuations. In this contribution, our aim is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantifier particularly robust in a noisy environment. The permutation entropy is defined as a functional of a symbolic probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantifies the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantifier, we compare with the results obtained by using a more standard chaos quantifier, namely the KolmogorovSinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at specific time-scales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The influence of additive observational noise on the proposed tool is also investigated.L.Z. and O.A.R. were supported by Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas (CONICET), Argentina. O.A.R. is PVE fellowship, CAPES, Brazil. Part of this work was funded by MEC (Spain), MICINN (Spain) and FEDER under Projects TEC2009-14101 (DeCoDicA) and FIS2007-60327 (FISICOS), and by the EC Project PHOCUS Grant 240763.Peer reviewe

A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line

A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations

The shifted Jacobi-Gauss collocation (SJGC) scheme is proposed and implemented to solve the fractional neutral functional-differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm

Nonlinear oscillations and chaos in chemical cardiorespiratory control

We report progress made on an analytic investigation of low-frequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemically-mediated blood-gas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate numerous (and more heuristic) extant efforts in the literature. Some of the physiologically-relevant behaviour obtained here has therefore been reported before, but a large number of features are reported for the first time. A particular novelty is the explicit demonstration of cardiorespiratory coupling via chemosensory control. The physiology and literature reviewed in Chapters 1 and 2 set the stage for the investigation. Chapter 3 scales and simplifies the Grodins model; Chapters 4, 5, 6 consider carbon dioxide dynamics at the central chemoreceptor. Chapter 7 begins analysis of the dynamics mediated by the peripheral receptor. Essentially all of the dynamical behaviour is due to the effect of time delays occurring within the conservation relations (which are ordinary differential equations). The pathophysiology highlighted by the analysis is considerable, and includes central nervous system disorders, heart failure, metabolic diseases, lung disorders, vascular pathologies, physiological changes during sleep, and ascent to high altitude. Chapter 8 concludes the thesis with a summary of achievements and directions for further work

An Application of Dynamical System in Forecasting Motorway Traffic flow

Circumstance is essentially too surely understood to every one of us. You're on your route, when out of nowhere you're stuck in traffic. It isn't an average "rush hour" time and ordinarily you do not worry about traffic jam. There must be a mishap or some kind of genuine accident up ahead. You slowly advance your way, heavily congested, always endeavoring to discover the blazing lights of ambulances and squad cars. At that point quickly, activity begins to move ordinarily once more. There's no sign of a mishap, episode, or whatever other reason for the slowing down in traffic. So what happened? Traffic Flow system is a human-joined, variable, open and cacheable framework. It is very nonlinear and uncertain. Under certain circumstance, disorder shows up in it. The overview of publish studies implicates the importance of finding and detecting disorders in traffic. Furthermore, the outline of procedures to recognize chaotic features - disorders in traffic flow and to forecast them demonstrates the requirement on current techniques and angle of study

Generalized Volterra-Wiener and surrogate data methods for complex time series analysis

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 133-150).This thesis describes the current state-of-the-art in nonlinear time series analysis, bringing together approaches from a broad range of disciplines including the non-linear dynamical systems, nonlinear modeling theory, time-series hypothesis testing, information theory, and self-similarity. We stress mathematical and qualitative relationships between key algorithms in the respective disciplines in addition to describing new robust approaches to solving classically intractable problems. Part I presents a comprehensive review of various classical approaches to time series analysis from both deterministic and stochastic points of view. We focus on using these classical methods for quantification of complexity in addition to proposing a unified approach to complexity quantification encapsulating several previous approaches. Part II presents robust modern tools for time series analysis including surrogate data and Volterra-Wiener modeling. We describe new algorithms converging the two approaches that provide both a sensitive test for nonlinear dynamics and a noise-robust metric for chaos intensity.by Akhil Shashidhar.M.Eng