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Nonlinear coherent states for the Susskind-Glogower operators

ROBERTO DE JESUS LEON MONTIEL (2010)

In this thesis, we construct nonlinear coherent states for the Susskind-Glogower

operators by the application of the displacement operator on the vacuum state.

We also construct nonlinear coherent states as eigenfunctions of a Hamiltonian

constructed with the Susskind-Glogower operators. We generalize the solution

to the eigenfunction problem to an arbitrary jmi initial condition. To analize

the obtained results, we plot the Husimi Q function, the photon number

probability distribution and the Mandel Q-parameter. For both cases, we nd

that the constructed states exhibit interesting nonclassical features such as

amplitude squeezing and quantum inteferences due to a self-splitting into two

coherent-like states. Additionally, we show that nonlinear coherent states may

be modelled by propagating light in semi-innite arrays of optical bers.

En la presente tesis, construímos estados coherentes no lineales para los operadores

de Susskind-Glogower mediante la aplicación del operador de desplazamiento

al estado de vacío. Construímos estados no lineales como eigenfunciones

de un Hamiltoniano construído con los operadores de Susskind-Glogower. Generalizamos

la solución al problema de eigenfunciones para una condición

inicial arbitraria jmi. Para analizar los resultados obtenidos, graficamos la

función Q de Husimi, la distribución de fotones y el parámetro Q de Mandel.

En ambos casos, encontramos que los estados construídos presentan características

no lineales tales como compresión en amplitud e interferencia cuántica

debida a la separación del estado en dos estados semejantes a los estados coherentes.

Adicionalmente, mostramos que los estados coherentes no lineales

pueden ser modelados mediante luz propagada en arreglos semi-innitos de

bras ópticas.

Master thesis

Quantum optics Coherent states Nonlinear systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ÓPTICA

Observatility and observers for nonlinear systems with time delays

Luis Alejandro Márquez Martínez (2002)

"Basic properties on linearization by output injection are investigated in this paper. A special structure is sought which is linear up to a suitable output injection and under a suitable change of coordinates. It is shown how an observer may be designed using theory available for linear time delay systems."

Article

Nonlinear systems with time delays, Nonlinear systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

Diseño analógico de osciladores caóticos basados en mapeos unidimensionales

JENNIFER VANESSA MARQUINA PEREZ (2008)

The phenomenon of chaos has become increasingly observed in the behaviour of myriad nonlinear deterministic system. Deterministic chaos can be defined as the phenomenon which is present in systems purely deterministic at the beginning, but they can show an unpredictable behaviour with the appropriate conditions. The simplest systems which show chaotic behaviour are discrete unidimensional maps. These systems are an excellent choice for electronic implementation due to their mathematical simplicity. In this thesis we present the design of two CMOS chaotic analog oscillators based on Logistic map and Bernoulli map, respectively. Using the mechanical statistics tools, such as bifurcation diagram and Lyapunov exponent, the design requirements of such oscillators are established

El comportamiento caótico es un fenómeno observado en una infinidad de sistemas determinísticos no lineales. El caos determinista se define como el fenómeno que se presenta en sistemas que son deterministas en un principio, pero que llegan a tener un comportamiento impredecible con las condiciones apropiadas. Los sistemas más simples que muestran caos son los mapeos unidimensionales discretos. Debido a la simplicidad matemática que presentan estos sistemas, son una excelente opción para su implementación en circuitos electrónicos. En este trabajo de tesis se presenta el diseño de dos osciladores caóticos analógicos CMOS, basados en el mapeo Logístico y el mapeo de Bernoulli. Mediante el uso de las herramientas de la mecánica estadística, como son el diagrama de bifurcación y el exponente de Lyapunov, se establecen los criterios de diseño para dichos osciladores

Master thesis

Chaos generators Analogue circuits Nonlinear dynamical systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA MICROELECTRÓNICA

Multiscroll attractors by switching systems

ERIC CAMPOS CANTON JUAN GONZALO BARAJAS RAMIREZ GUALBERTO CELESTINO SOLIS PERALES ALEJANDRO RICARDO FEMAT FLORES (2010)

"In this paper, we present a class of three-dimensional dynamical systems having multiscrolls which we call unstable dissipative systems (UDSs). The UDSs are dissipative in one of its components but unstable in the other two. This class of systems is constructed with a switching law to display various multiscroll strange attractors. The multiscroll strange attractors result from the combination of several unstable "one-spiral" trajectories by means of switching. Each of these trajectories lies around a saddle hyperbolic stationary point. Thus, we describe how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior."

Article

Chaos Differential equations; Nonlinear dynamical systems; Synchronisation CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

Diseño de osciladores caóticos integrados

HUGO DE LEON HIDALGO (2008)

Continuous time chaotic oscillators are a special type of nonlinear systems that shows an aperiodic behavior and a continuous wide band. This characteristic is very attractive in some applications like spread spectrum communications.

Since first discoveries of this behavior until nowadays, there has been a wide searching in trying to understand its dynamics and functioning, in looking for new schemes of chaotic circuits and trying to control it.

Because of continuous time chaotic oscillators applications are realized through integrated circuits, this work focuses to the development of integrated circuits chaotic oscillators. It has been realized some efforts in the matter of integrating chaotic oscillators. However, most of them are implemented through the state variable method that shows that transforms the circuit in a different form using integrators, multipliers and other devices additional to the circuit. This has the disadvantage that increases the area, power consumption, noise and cost. On the other hand, the direct realization of the circuit shows some challenges like the reduced robustness of some chaotic oscillators when their dynamic elements are taken to the range of integration values or the lack of chaotic behavior in this range of their parameters. This, added to the inherent problems of integrated circuits such as parasitic elements and nonlinearities make almost impossible the direct realization of chaotic oscillators on integrated circuits.

This work introduces a new technique that allows the direct integration of chaotic circuits. The technique consists in the introduction of a periodic oscillator inside the nonlinear resistance of the chaotic oscillator. The resulting effect is the increasing in the mixing of the trajectories in the phase space description and of the robustness of the circuit against the variation on the element values and parasitic. All these, allows the realization of robust integrated chaotic circuits.

They are shown three cases of chaotic circuits in order to exemplify the technique. Nonlinear resistances are realized through models of different levels of abstraction and through a new architecture of second generation “current conveyor” proposed

in this work that shows a periodic behavior and allows us to demonstrate the method.

The knowledge generated by this work was traduced in the conception of a new chaotic oscillator that was fabricated. Results of measurements of the circuit are compared with simulation

Los osciladores caóticos continuos en el tiempo son un tipo especial de circuitos no lineales que se comportan de manera aperiódica, por lo que presentan un banda continua, extendida en un amplio rango del espectro de frecuencias. Esta característica parece ser atractiva en algunas aplicaciones, sobre todo en el área de comunicaciones de espectro extendido. Desde los primeros descubrimientos de este comportamiento hasta nuestro días, ha habido una amplia investigación de estos circuitos tratando de comprender su dinámica y mecanismo de funcionamiento, introduciendo nuevos esquemas de circuitos que presenten el comportamiento, formas nuevas de controlarlo, etc. Debido a que las aplicaciones de los osciladores caóticos continuos en el tiempo se realizan a través de circuitos integrados, este trabajo se enfoca al tema del desarrollo de circuitos osciladores caóticos integrados en chip. Se han realizado algunos esfuerzos por integrar este tipo de circuitos. Sin embargo, la mayoría de ellos los implementa a través del método de variables de estado, que transforma el circuito en una forma diferente, usando integradores, sumadores, multiplicadores, etc. Esto tiene muchas desventajas por que incrementa el número de dispositivos necesarios para realizarlo y con ello incrementa el área, consumo de potencia, ruido y por consiguiente el costo. Por el otro lado, la realización directa de estos circuitos presenta muchos desafíos pues algunos de ellos reducen su robustez al llevar el valor de sus elementos dinámicos a la región de integración, y otros simplemente no presentan comportamiento caótico en esta región. Esto, aunado a los problemas inherentes de los circuitos integrados, como parásitas y no linealidades, hace casi imposible la realización directa de los osciladores caóticos en circuitos integrados. En este trabajo se presenta una técnica que permite integrar osciladores caóticos de manera directa. La técnica consiste en la inclusión de un oscilador periódico dentro de la resistencia no lineal. Esto tiene el efecto de incrementar el mezclado de las trayectorias en el espacio de fase y de robustecer al circuito contra las variaciones de los valores de los elementos y las parásitas del mismo, lo que permite la realización de circuitos caóticos integrados robustos. Se presentan tres casos específicos de circuitos para ejemplificar la técnica.

Doctoral thesis

Chaos Integrated circuit design Nonlinear dynamical systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA DISEÑO DE CIRCUITOS

Estimates of the attraction region for a class of nonlinear time-delay systems

DANIEL ALEJANDRO MELCHOR AGUILAR Silviu Iulian Niculescu (2007)

"In this paper, we propose various estimates of the attraction region for a class of nonlinear time-delay systems of the form forumla The approach is constructive and makes use of a Lyapunov–Krasovskii functional associated to the linear part. Several illustrative examples (delayed logistic equation, stabilizing nonlinear oscillations by delayed output feedback, congestion control in high-performance networks and hereditary phenomena in physics) complete the presentation."

Article

Nonlinear time-delay systems Attraction region Lyapunov-Krasovskii functionals CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA MATEMÁTICAS

Nonlinear voltage regulation strategy for a fuel cell/supercapacitor power source system

Yuz Asaf Zúñiga Ventura Jesús Leyva Ramos LUIS HUMBERTO DIAZ SALDIERNA Irwin Allen Díaz Díaz DIEGO LANGARICA CORDOBA (2018)

"The main purpose of this work is to model and control a fuel cell/supercapacitor power source system to feed a DC-bus with a constant output voltage despite load changes. The fuel cell is modeled as a nonlinear current-dependent voltage source meanwhile, the supercapacitor is represented as an ideal capacitor. The power converters are modeled using a average model techniques. Furthermore, the proposed nonlinear state feedback control method is based on backstepping techniques and Lyapunov stability analysis to ensure that error signals converge to zero. A load estimator is designed using Immersion-Invariance (I&I) theory to track load changes through available measurements. Finally, simulation results show that the proposed control scheme stabilizes the system when step changes are applied to the load."

Article

Fuel cell Supercapacitor DC-DC power converter Nonlinear control systems INGENIERÍA Y TECNOLOGÍA INGENIERÍA Y TECNOLOGÍA

Note sur l'accessibilité des systèmes non linéaires à retards

LUIS ALEJANDRO MARQUEZ MARTINEZ (1999)

"In this paper, the accessibility for nonlinear time-delay systems is considered for the first time. A suitable definition is proposed and a sufficient condition to test if a given system is accessible is stated."

Article

Nonlinear time-delay systems, Time-Delay, Nonlinear CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA FÍSICA ELECTRÓNICA

Multifractal properties of elementary cellular automata in a discrete wavelet approach of MF-DFA

JAIME ENRIQUE PEREZ TERRAZAS HARET CODRATIAN ROSU (2009)

"In 2005, Nagler and Claussen (Phys. Rev. E 71, 067103 (2005)) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. They eliminated the polynomial background atb through the direct fit-ting of the polynomial coefficients a and b. We here reconsider their work eliminating the polynomial trend by means of the multifractal-based detrended fluctuation analysis (MF-DFA) in which the wavelet multiresolution property is employed to filter out the trend in a more speedy way than the direct polynomial fitting and also with respect to the wavelet transform modulus maxima (WTMM) procedure. In the algorithm, the discrete fast wavelet transform is used to calculate the trend as a local feature that enters the so-called details signal. We illustrate our result for three representative ECA rules: 90, 105, and 150. We confirm their multifractal behavior and provide our results for the scaling parameters."

Article

Statistical physics and nonlinear systems CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA

FRW barotropic zero modes: dynamical systems observability

HARET CODRATIAN ROSU VRANI IBARRA JUNQUERA (2007)

"The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmolo-gies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode nor of its derivative as dy-namical cosmological states. Only knowing the latter ones correspond to a rigorous dynamical observability in barotropic cosmology."

Article

Supersymmetry FRW barotropic cosmology (Nonlinear) dy-namical systems observability CIENCIAS FÍSICO MATEMÁTICAS Y CIENCIAS DE LA TIERRA