Hybrid analysis of nonlinear circuits: DAE models with indices zero and one

We extend in this paper some previous results concerning the differential-algebraic index of hybrid models of electrical and electronic circuits. Specifically, we present a comprehensive index characterization which holds without passivity requirements, in contrast to previous approaches, and which applies to nonlinear circuits composed of uncoupled, one-port devices. The index conditions, which are stated in terms of the forest structure of certain digraph minors, do not depend on the specific tree chosen in the formulation of the hybrid equations. Additionally, we show how to include memristors in hybrid circuit models; in this direction, we extend the index analysis to circuits including active memristors, which have been recently used in the design of nonlinear oscillators and chaotic circuits. We also discuss the extension of these results to circuits with controlled sources, making our framework of interest in the analysis of circuits with transistors, amplifiers, and other multiterminal devices.

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Theory of intermittency applied to classical pathological cases

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Though it works fine in some model systems, there exist a number of so-called pathological cases characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. Recently, we reported on how the reinjection probability density (RPD) can be generalized. Here, we extend this methodology and apply it to different dynamical systems exhibiting anomalous type-II and type-III intermittencies. Estimation of the universal RPD is based on fitting a linear function to experimental data and requires no a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets (dozens of points). Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. We show that the method copes well with dynamical systems exhibiting significantly different statistics reported in the literature. We also derive and classify characteristic relations between the mean laminar length and main controlling parameter in perfect agreement with data provided by numerical simulations

El imaginario en la génesis del proyecto arquitectónico: La construcción de la realidad a través del mito, la utopía y la cibercultura

El término imaginario, nombra el principio y el tema central de una investigación del mundo arquitectónico, necesaria para entender las condiciones alrededor de un proceso proyectual íntimo, cargado de significaciones ideológicas y simbólicas. En diferentes interpretaciones, el inconsciente colectivo y personal, científico o social, aparece en el origen de cada pensamiento y comportamiento humano, constituyendo un universo cerrado y caótico, donde todas las ideas están en constante tensión y contradicción. Por esta razón existen nociones y construcciones lógicas y coherentes que estructuran el marco de la verisimilitud y por tanto el régimen de la realidad, mediante la verdad y la verificación. Para el proyecto arquitectónico estas configuraciones se expresan en la situación del espacio, el tiempo y el cuerpo, como elementos básicos de jerarquización de la habitabilidad y de la cohabitabilidad humana. Esta tesis pretende acotar y definir un ámbito de procesos verosímiles instalados dentro del imaginario mediante el patrimonio intangible del pensamiento mítico o utópico, donde no solamente se crean envolventes del pensamiento, de iconografía o de sociedades, sino de donde también se derivan modelos rígidos y excluyentes, desde teorías basadas en la heteronormatividad y la segregación según el sexo, el género, la clase y la capacidad dentro de la diversidad funcional. La experiencia del espacio arquitectónico ha sido tradicionalmente descrita mediante palabras e imágenes: el lógos y el símbolo han sido los grandes intermediadores entre los sujetos y el habitar. Los ámbitos cotidiano y urbano se han regido por modelos y normas absolutas aplicadas universalmente y el mundo arquitectónico se ha visto estancado en la polaridad dual, entre lo público y lo privado, el dentro y el fuera, el movimiento y el reposo, el hombre y la mujer. Si el espacio-tiempo, el cuerpo y sus interpretaciones son la base para los modelos absolutistas, universalistas y perfeccionistas que han dominado el pensamiento occidental y elaborado la noción de lo “normal” en su totalidad, restando complejidad y diversidad, en la era hipermoderna ya no tiene sentido hablar en términos que no contemplen la superposición y la contradicción de la multiplicidad caótica en igualdad y en equilibrio instable. La realidad se ha visto reinventada a través de situaciones intermedias, los lugares inbetween en los espacios, tiempos, identidades y nociones presupuestas, donde se ha tergiversado el orden establecido, afectando al imaginario. La cotidianidad ha superado la arquitectura y el tiempo ha aniquilado el espacio. La conectividad, las redes y el libre acceso a la información – allá donde los haya – componen el marco que ha permitido a los sujetos subalternos emerger y empezar a consolidarse en el discurso teórico y práctico. Nuevos referentes están apareciendo en el hiper-espacio/tiempo aumentado, infringiendo todas aquellas leyes e interpretaciones impuestas para controlar los hábitos, las conductas y las personas. La casa, la ciudad y la metrópolis al vaciarse de contenidos, han dejado de cumplir funciones morales y simbólicas. Los no-lugares, los no-space, los no-time (Amann, 2011) son las condiciones radicalmente fenoménicas que reemplazan la realidad de lo vivido y activan de forma directa a los sentidos; son lugares que excitan el cuerpo como termótopos (Sloterdijk, 2002), que impulsan el crecimiento de la economía y en gran medida la multinormatividad. Sin duda alguna, aquí y ahora se requiere un nuevo modo de emplear la palabra, la imagen y la tecnología, dentro de una temporalidad efímera y eterna simultáneamente. ABSTRACT The term imaginary marks the beginning and the main topic of this research into the architectural world, presented as the necessary condition to understand the design process in its intimate layers, loaded with ideological and symbolic meanings. Through different interpretations, the unconscious, personal and collective, scientific or social, is found in the origin of every human thought and behaviour, constituting a closed chaotic universe, where all ideas are in constant tension and contradiction. This is why there are logical and coherent notions or discursive constructions which organise the context of verisimilitude and therefore the regime of reality through truth and its verification. For the architectural project, these specific configurations are associated with space, time and body as basic elements of management and hierarchization of human habitability and co-habitability. This thesis aims to demarcate and define a field of verisimilar processes installed in the imaginary, through the intangible heritage of mythical or utopian thinking, where not only enclosures of thought, iconography or utopian ideals are created, but from where rigid and exclusive models are derived as well, from theories based on heteronormativity and segregation by sex, gender, class and functional diversity. The experience of the architectural space has been described traditionally through words and images: the language and the symbol have been intermediating between the user and his habitat. Everyday life and urban interactions have been governed by absolute, universally applied, models or standards, therefore the architectural world has been stalled in a constant dual polarity between the public and the private, the inside and the outside, the movement and the repose, the man and the woman. Certainly, if the space-time notion, along with the theorization of the body, are the basis for absolutist, universalist and perfectionist models that have dominated western thought and developed the concept of “normal” in its totality, deducting all complexity and diversity, in the hypermodern era it makes no longer sense to speak in terms that ignore the overlap and contradiction of the chaotic multiplicity that characterises equality and unstable balance. Reality has been reinvented through intermediate situations, the in-between spaces, time, identities, or other presupposed notions. The order of truth has been distorted, affecting and transforming the contemporary imaginary. Everyday practices have surpassed the architectural design and time has annihilated space. Connectivity, networks, free access to information -wherever it exists-, compose the framework that has allowed subaltern subjectivity to emerge and begin to consolidate into main theoretical and practical discourses. New models are appearing in the augmented hyper-space/ time, transgressing any rule and interpretation imposed to control habits, behaviours and people. The house, the city and the metropolis are empty of content; they no longer fulfil moral and symbolic functions. The non-places, non-space, non-time (Amann, 2011) are radically phenomenal conditions that replace the reality of the lived experience and activate the senses as places that excite the body, thermotopos (Sloterdijk, 2002), which boost economic growth and to a considerable extent the multinormativity. Undoubtedly, what is required here and now is a new way of employing the word, the image and the technology within an ephemeral yet eternal temporality.

Chaos in non lineal Alfven waves using the DNLS equations

The electro-dynamical tethers emit waves in structured denominated Alfven wings. The Derivative Nonlineal Schrödinger Equation (DNLS) possesses the capacity to describe the propagation of circularly polarized Alfven waves of finite amplitude in cold plasmas. The DNLS equation is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In this article is presented a theoretical and numerical analysis when the growth rate of the unstable wave is next to zero considering two damping models: Landau and resistive. The DNLS equation presents a chaotic dynamics when is consider only three wave truncation. The evolution to chaos possesses three routes: hard transition, period-doubling and intermittence of type I.

Digital chaos synchronization in optical networks

A possible approach to the synchronization of chaotic circuits is reported. It is based on an Optically Programmable Logic Cell and as a consequence its output is digital, its application to cryptography in Optical Communications comes directly from its properties. The model here presented is based on a computer simulation.

Dynamics of gas bubbles encapsulated by a viscoelastic fluid shell under acoustic fields

The dynamics of a gas-filled microbubble encapsulated by a viscoelastic fluid shell immersed in a Newtonian liquid and subject to an external pressure field is theoretically studied. The problem is formulated by considering a nonlinear Oldroyd type constitutive equation to model the rheological behavior of the fluid shell. Heat and mass transfer across the surface bubble have been neglected but radiation losses due to the compressibility of the surrounding liquid have been taken into account. Bubble collapse under sudden increase of the external pressure as well as nonlinear radial oscillations under ultrasound fields are investigated. The numerical results obtained show that the elasticity of the fluid coating intensifies oscillatory collapse and produces a strong increase of the amplitudes of radial oscillations which may become chaotic even for moderate driving pressure amplitudes. The role played by the elongational viscosity has also been analyzed and its influence on both, bubble collapse and radial oscillations, has been recognized. According to the theoretical predictions provided in the present work, a microbubble coated by a viscoelastic fluid shell is an oscillating system that, under acoustic driving, may experience volume oscillations of large amplitude, being, however, more stable than a free bubble. Thus, it could be expected that such a system may have a suitable behavior as an echogenic agent.

Characterizing chaos in a type of fractional duffing's equation

We characterize the chaos in a fractional Duffing’s equation computing the Lyapunov exponents and the dimension of the strange attractor in the effective phase space of the system. We develop a specific analytical method to estimate all Lyapunov exponents and check the results with the fiduciary orbit technique and a time series estimation method.

Cifrado de imágenes digitales basado en teoría del caos: mapas logísticos

Las nuevas tendencias de compartir archivos multimedia a través de redes abiertas, demanda el uso de mejores técnicas de encriptación que garanticen la integridad, disponibilidad y confidencialidad, manteniendo y/o mejorando la eficiencia del proceso de cifrado sobre estos archivos. Hoy en día es frecuente la transferencia de imágenes a través de medios tecnológicos, siendo necesario la actualización de las técnicas de encriptación existentes y mejor aún, la búsqueda de nuevas alternativas. Actualmente los algoritmos criptográficos clásicos son altamente conocidos en medio de la sociedad informática lo que provoca mayor vulnerabilidad, sin contar los altos tiempos de procesamiento al momento de ser utilizados, elevando la probabilidad de ser descifrados y minimizando la disponibilidad inmediata de los recursos. Para disminuir estas probabilidades, el uso de la teoría de caos surge como una buena opción para ser aplicada en un algoritmo que tome partida del comportamiento caótico de los sistemas dinámicos, y aproveche las propiedades de los mapas logísticos para elevar el nivel de robustez en el cifrado. Es por eso que este trabajo propone la creación de un sistema criptográfico basado sobre una arquitectura dividida en dos etapas de confusión y difusión. Cada una de ellas utiliza una ecuación logística para generar números pseudoaleatorios que permitan desordenar la posición del píxel y cambiar su intensidad en la escala de grises. Este proceso iterativo es determinado por la cantidad total de píxeles de una imagen. Finalmente, toda la lógica de cifrado es ejecutada sobre la tecnología CUDA que permite el procesamiento en paralelo. Como aporte sustancial, se propone una nueva técnica de encriptación vanguardista de alta sensibilidad ante ruidos externos manteniendo no solo la confidencialidad de la imagen, sino también la disponibilidad y la eficiencia en los tiempos de proceso.---ABSTRACT---New trends to share multimedia files over open networks, demand the best use of encryption techniques to ensure the integrity, availability and confidentiality, keeping and/or improving the efficiency of the encryption process on these files. Today it is common to transfer pictures through technological networks, thus, it is necessary to update existing techniques encryption, and even better, the searching of new alternatives. Nowadays, classic cryptographic algorithms are highly known in the midst of the information society which not only causes greater vulnerability, but high processing times when this algorithms are used. It raise the probability of being deciphered and minimizes the immediate availability of resources. To reduce these odds, the use of chaos theory emerged as a good option to be applied on an algorithm that takes advantage of chaotic behavior of dynamic systems, and take logistic maps’ properties to raise the level of robustness in the encryption. That is why this paper proposes the creation of a cryptographic system based on an architecture divided into two stages: confusion and diffusion. Each stage uses a logistic equation to generate pseudorandom numbers that allow mess pixel position and change their intensity in grayscale. This iterative process is determined by the total number of pixels of an image. Finally, the entire encryption logic is executed on the CUDA technology that enables parallel processing. As a substantial contribution, it propose a new encryption technique with high sensitivity on external noise not only keeping the confidentiality of the image, but also the availability and efficiency in processing times.

De la desintegración Espacial a la Conformación regional en la Sabana de Bogotá. Una Propuesta para el desarrollo de la Ciudad Región en el siglo XXI

El presente trabajo de investigación aborda el tema del desarrollo regional en torno a una gran metrópoli como Bogotá y la Sabana de Bogotá. El crecimiento, expansión y relación con los municipios vecinos. Su entorno territorial; es un tema de discusión que cada día adquiere más fuerza desde hace varias décadas. Bogotá y la Sabana de Bogotá, se consideran en la actualidad como un caso representativo del caótico modelo de expansión urbana y crecimiento demográfico, enfrentado al desarrollo urbano como paradigma de la desigualdad de la ciudad latinoamericana. Son muchos los procesos y conflictos de naturaleza Regional y metropolitana que atraviesa la capital colombiana. Sin embargo esta investigación abordada el tema desde la necesidad de gobernanza y coordinación para el desarrollo territorial consensuado y equilibrado de la Región. La sabana de Bogotá está conformada por ciudades dormitorio, ciudades industriales, turísticas, agropecuarias, etc., es atravesada por el Río Bogotá, y en su centro la gran metrópoli, Bogotá D.C. centro de trabajo muy importante a nivel nacional, su área de influencia más próxima llega hasta: Caqueza, Zipaquira, Facatativa, Soacha, Fusagasuga y Girardot. Principales polos de desarrollo en la sabana y el departamento. Cundinamarca está compuesto por 15 provincias y Bogotá. Conformando un sistema de redes urbanas con necesidades comunes y demanda servicios públicos, de transporte, aseo, movilidad, salud, educación, espacio público y calidad ambiental. La metodología de esta investigación consiste en el análisis de la región a partir de la articulación de planes de ordenamiento territorial en un área de estudio propuesta. Mediante entrevistas con profesionales, expertos, funcionarios y empleados públicos y teniendo en cuenta las posibilidades legales en Colombia para el desarrollo territorial regional, establecer la situación real en materia de desarrollo para el departamento de Cundinamarca, evidenciando las necesidades del territorio y su desarrollo de una forma más compleja, valorando las sinergias y necesidades sociales, ambientales y económicas propias del crecimiento urbano, para proponer una serie de directrices que estructuren un desarrollo regional equilibrado en Bogotá y Cundinamarca. El análisis de los modelos del caso contribuye a fortalecer iniciativas para el desarrollo Regional de la Sabana de Bogotá como territorio sostenible: ambiental, económico y socialmente. En un sistema de redes que interconecte a Bogotá, con Cundinamarca, Colombia y el resto del mundo. Cundinamarca como región debe fijar estrategias y articular políticas en función de un modelo de desarrollo urbano regional para el departamento y la Sabana de Bogotá. Directrices departamentales básicas y fundamentales para el desarrollo territorial equilibrado que promueva ciudades sostenibles, compactas y con Calidad de vida para todos sus habitantes. ABSTRACT: This research addresses the issue of regional development around a big metropolis like Bogotá and Sabana de Bogota. The growth, expansion and relations with neighboring municipalities. Your local environment; It is an issue that becomes stronger every day for decades. Bogotá and Sabana de Bogotá, are considered today as a representative case of the chaotic model of urban expansion and population growth, urban development faced as a paradigm of inequality in Latin American city. Many processes and conflicts of Regional and metropolitan nature that crosses the Colombian capital. However this research addressed the issue from the need for governance and coordination for consensual and balanced territorial development of the region. The savannah of Bogota consists of bedroom communities, industrial cities, tourism, agriculture, etc., is crossed by the Bogota River, and at its center the great metropolis, Bogota DC center very important work at the national level, the area closest influence reaches: Caqueza, Zipaquira, Facatativa, Soacha, Fusagasuga and Girardot. Main centers of development in the savannah and the department. Cundinamarca is composed of 15 provinces and Bogota. Forming a system of urban networks with common needs and demand utilities, transportation, grooming, mobility, health, education, public space and environmental quality. The methodology of this research is the analysis of the region from the joint land use plans in the proposed study area. Through interviews with professionals, experts, public officials and employees and taking into account the legal possibilities in Colombia for regional territorial development, establish the real situation in development for the department of Cundinamarca, showing the region's needs and development of a more complex form, assessing synergies and own social, environmental and economic needs of urban growth, to propose a set of guidelines to structure a balanced regional development in Bogota and Cundinamarca. The analysis of case models helps to strengthen initiatives for regional development of the Sabana de Bogota and sustainable region: environmentally, economically and socially. In a network system that interconnects to Bogotá with Cundinamarca, Colombia and elsewhere. Cundinamarca region should set as joint strategies and policies based on a model of regional urban development for the department and the Sabana de Bogota. Basic and fundamental to balanced territorial development that fosters sustainable, compact and quality of life for all its inhabitants cities departmental guidelines.