Control of bistability in a directly modulated semiconductor laser using delayed optoelectronic feedback

We show numerically that direct delayed optoelectronic feedback can suppress hysteresis and bistability in a directly modulated semiconductor laser. The simulation of a laser with feedback is performed for a considerable range of feedback strengths and delays and the corresponding values for the areas of the hysteresis loops are calculated. It is shown that the hysteresis loop completely vanishes for certain combinations of these parameters. The regimes for the disappearance of bistability are classified globally. Different dynamical states of the laser are characterized using bifurcation diagrams and time series plots.

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.

Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Evidence for the existence of Sarkovskii ordering in a two-dimensional map

We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.

Universal behaviour in a ``modulated'' logistic map

We study the period-doubling bifurcations to chaos in a logistic map with a nonlinearly modulated parameter and show that the bifurcation structure is modified significantly. Using the renormalisation method due to Derrida et al. we establish the universal behaviour of the system at the onset of chaos.

Multifractal dimension of chaotic attractors in a driven semiconductor superlattice

The multifractal dimension of chaotic attractors has been studied in a weakly coupled superlattice driven by an incommensurate sinusoidal voltage as a function of the driving voltage amplitude. The derived multifractal dimension for the observed bifurcation sequence shows different characteristics for chaotic, quasiperiodic, and frequency-locked attractors. In the chaotic regime, strange attractors are observed. Even in the quasiperiodic regime, attractors with a certain degree of strangeness may exist. From the observed multifractal dimensions, the deterministic nature of the chaotic oscillations is clearly identified.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

" Nonlinear Signal Processing of Electroencephalogram .' Application in the Study of Neurodynamics. "

Interfacings of various subjects generate new field ofstudy and research that help in advancing human knowledge. One of the latest of such fields is Neurotechnology, which is an effective amalgamation of neuroscience, physics, biomedical engineering and computational methods. Neurotechnology provides a platform to interact physicist; neurologist and engineers to break methodology and terminology related barriers. Advancements in Computational capability, wider scope of applications in nonlinear dynamics and chaos in complex systems enhanced study of neurodynamics. However there is a need for an effective dialogue among physicists, neurologists and engineers. Application of computer based technology in the field of medicine through signal and image processing, creation of clinical databases for helping clinicians etc are widely acknowledged. Such synergic effects between widely separated disciplines may help in enhancing the effectiveness of existing diagnostic methods. One of the recent methods in this direction is analysis of electroencephalogram with the help of methods in nonlinear dynamics. This thesis is an effort to understand the functional aspects of human brain by studying electroencephalogram. The algorithms and other related methods developed in the present work can be interfaced with a digital EEG machine to unfold the information hidden in the signal. Ultimately this can be used as a diagnostic tool.

Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Transport of Sub-micron Aerosols in Bifurcations

The convective-diffusive transport of sub-micron aerosols in an oscillatory laminar flow within a 2-D single bifurcation is studied, using order-of-magnitude analysis and numerical simulation using a commercial software (FEMLAB®). Based on the similarity between momentum and mass transfer equations, various transient mass transport regimes are classified and scaled according to Strouhal and beta numbers. Results show that the mass transfer rate is highest at the carinal ridge and there is a phase-shift in diffusive transport time if the beta number is greater than one. It is also shown that diffusive mass transfer becomes independent of the oscillating outer flow if the Strouhal number is greater than one.

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Exercise sheet 1

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Application of agent-based modeling to the study of gender stereotypes

Gender stereotypes are sets of characteristics that people believe to be typically true of a man or woman. We report an agent-based model (ABM) that simulates how stereotypes disseminate in a group through associative mechanisms. The model consists of agents that carry one of several different versions of a stereotype, which share part of their conceptual content. When an agent acts according to his/her stereotype, and that stereotype is shared by an observer, then the latter’s stereotype strengthens. Contrarily, if the agent does not act according to his/ her stereotype, then the observer’s stereotype weakens. In successive interactions, agents develop preferences, such that there will be a higher probability of interaction with agents that confirm their stereotypes. Depending on the proportion of shared conceptual content in the stereotype’s different versions, three dynamics emerge: all stereotypes in the population strengthen, all weaken, or a bifurcation occurs, i.e., some strengthen and some weaken. Additionally, we discuss the use of agent-based modeling to study social phenomena and the practical consequences that the model’s results might have on stereotype research and their effects on a community

Construcción de una filogenia molecular para las especies de los géneros Klebsiella y Raoultella basada en los genes ARNr 16S y ARN polimerasa subunidad

Las bacterias de los géneros Raoultella y Klebsiella son patógenos oportunistas para las cuales no existe un sistema uniforme de clasificación taxonómica internacional. En el presente estudio se propone una filogenia molecular basada en el gen ribosomal 16S (ADNr 16S) y el gen codificante de la subunidad de la ARN polimerasa (rpoB) de los géneros Klebsiella y Raoultella con el fin de establecer relaciones evolutivas entre dichos géneros. Los resultados evidencian una agrupación acorde con la taxonomía y las propiedades bioquímicas características, reportadas en el Genbank. Se estableció una bifurcación en los árboles, lo cual confirma la separación de los géneros Klebsiella y Raoultella. Adicionalmente, se confirmó el carácter polifilético de K. aerogenes por el gen ADNr 16S y la agrupación de R. terrigena y K. oxytoca de acuerdo con el gen rpoB. La comparación entre los árboles obtenidos permitió determinar relaciones evolutivas entre las especies, a partir de los genes evaluados, lo cual refleja cambios aparentes a nivel taxonómico y corrobora la importancia del análisis a nivel de multilocus. Este tipo de estudios permite monitorear la estabilidad de los genotipos microbianos sobre la escala temporal y espacial, mejorar la precisión de las anotaciones taxonómicas (mejor descripción de taxones o subdivisiones genéticas) y evaluar la diversidad genética y adaptabilidad en términos de virulencia o resistenciaa drogas.

GESTIÓN CON BASE EN LAS CIENCIAS DE LA COMPLEJIDAD: LAS ORGANIZACIONES COMO ESTUCTURAS DISIPATIVAS

Resumen: Este texto explora el sentido y la posibilidad de introducir la teoría de Ilya Prigogine “estructuras disipativas” en el contexto de las organizaciones. La tesis aquí propuesta afirma que las organizaciones son sistemas abiertos, alejados del equilibrio y tiene que ver con posibilidades creativas, antes que con realidades fácticas. Por lo tanto, las organizaciones de no-equilibrio están constituidas por fenómenos de comportamientos espontáneos o coherentes que reclaman para sobrevivir cierta disipación de energía y, por tanto, el mantenimiento de una interacción con el mundo exterior. Con ello la gerencia adquiere un papel destacado en el estudio de las organizaciones como estructuras disipativas encaminadas a generar y permitir el Biodesarrollo. Palabras claves: Estructuras Disipativas, Fluctuaciones, Bifurcaciones, Gerencia, Biodesarrollo, Auto-eco-organizador. Abstract:  This text explores the sense and possibility of introducing Ilya Prigogine´s theory “dissipative structures”, into organizations´ context. The thesis proposed here states that organizations are open systems which are far away from equilibrium and had to deal with creative possibilities before being practical realities. Thus, no-equilibrium organizations are made of spontaneous or coherent behavioral phenomenon that strives to survive a certain amount of energy loss, hence the maintenance of interaction with external world. This way organizations management acquires an outstanding roll in studying organizations as dissipative structures prone to create and allow bio-development.Key Words: Dissipative Structures, Fluctuation, Bifurcation, Management, Bio-development, eco-self-organizer.