Luz del Carmen Gómez-Pavón

Determining the Lyapunov Spectrum of Continuous-Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution of -PWL Variational Equations

An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from -piecewise linear variational equations and their associated -Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.

Synchronization of multi-directional multi-scroll chaos generators: A Hamiltonian approach

In this paper, a chaotic synchronization scheme for multi-directional multi-scroll chaos generators is presented. We use Generalized Hamiltonian forms approach to determine the synchronization conditions for two unidirectionally coupled multi-directional multi-scroll chaotic attractors. First, two state-variables of the master system are used to control the two nonlinear functions in the slave system and consequently, reach the synchronization of two 2D-4-scroll chaotic systems. Similarly, the synchronization of two 3D-4-scroll chaotic systems is achieved by using all three state-variables in order to control the three nonlinear functions for the slave system. Finally, theoretical calculations are in good agreement with numerical simulations and a prediction on the values for observer gain is also given.

Tapered Optical Fiber Functionalized with Palladium Nanoparticles by Drop Casting and Laser Radiation for H2 and Volatile Organic Compounds Sensing Purposes

A comparative study on the sensing properties of a tapered optical fiber pristine and functionalized with the palladium nanoparticles to hydrogen and volatile organic compounds (VOCs), is presented. The sensor response and, response/recovery times were extracted from the measurements of the transient response of the device. The tapered optical fiber sensor was fabricated using a single-mode optical fiber by the flame-brushing technique. Functionalization of the optical fiber was performed using an aqueous solution of palladium chloride by drop-casting technique assisted for laser radiation. The detection principle of the sensor is based on the changes in the optical properties of palladium nanoparticles when exposed to reducing gases, which causes a variation in the absorption of evanescent waves. A continuous wave laser diode operating at 1550 nm is used for the sensor characterization. The sensor functionalized with palladium nanoparticles by this technique is viable for the sensing of hydrogen and VOCs, since it shows an enhancement in sensor response and response time compared to the sensor based on the pristine optical microfiber. The results show that the fabricated sensor is competitive with other fiber optic sensors functionalized with palladium nanoparticles to the hydrogen.

Self-compression of coupled cnoidal waves

In this work, the dynamics of a pulse train propagating through a bimodal optical fiber whose core refractive index varies periodically along its main axis are studied numerically. The mathematical model is based on a coupled system of nonlinear Schrodinger-like equations. First- and second-order dispersions are taken into account, as well as the number of solitons propagating through the fiber. The physical conditions for self-compression of coupled cnoidal waves are obtained and discussed.

Fault conditions of a simple chaotic circuit under capacitor nonlinear effects

In this paper a tolerance analysis in the electronic design of a simple chaos generator is reported. This simple chaotic oscillator is composed by four resistors, three capacitors and two opamps. A Verilog-A model for the opamps and capacitors is used herein. For the opamp, the model contains input impedance, finite bandwidth with a dominant pole and voltage saturation effects. In case of capacitor, a nonlinear model based on a varactor is considered, which includes the charge-dependence with the voltage. By using H-Spice simulator, the sensitivity of the chaos generation in the simple chaotic oscillator as a function of the varactor is analyzed. Several H-Spice simulations are given.

Determining the number of scrolls in a multi-scroll chaotic oscillator under uncertainties

A trade-off analysis on the chaotic regime in a multi-scroll chaotic system and the uncertainties of its parameters is presented. The chaotic oscillator is modeled by using the state-variables approximation and its nonlinear function is represented as a piecewise linear (PWL) function. In particular, a 4-scroll chaotic system with four parameters is studied. Due to the chaotic behavior depends on the system parameters; linear and random sweeps are performed to obtain an interval for each parameter. This trust interval is used to predict the number of scrolls that can be synthesized under uncertainties and also, the implementation with an electronic circuit based on operational amplifiers. MATLAB simulations confirm the usefulness of the proposed approach.

Behavioral Modeling of Chaos-Based Applications by Using Verilog-A

In general, a system can be defined as a collection of interconnected components that transforms a set of inputs received from its environment to a set of outputs. From an engineering point of view, chaos-based applications can be classified as a electronic system where the vast majority of the internal signals used as interconnections are electrical signals. Inputs and outputs are also provided as electrical quantities, or converted from, or to, such signals using sensors or actuators. To gain insight about the overall performance of the particular chaos-based application, the whole system must be characterized and simulated simultaneously. That is not a trivial task because the complexity of each one of the blocks that comprises the system, as well as the intrinsic complex behavior of chaotic generators. In this chapter, a modeling strategy suited to represent chaos-based applications for different control parameters of chaotic systems is presented. Based on behavioral descriptions obtained from a Hardware Description Language (HDL), called Verilog-A, two applications of chaotic systems are analyzed and designed. More specifically, a chaotic sinusoidal pulse width modulator (SPWM) which is useful to develop control algorithms for motor drivers in electric vehicles, and a chaotic pulse position modulator (CPPM) widely used in communication systems are presented as cases under analysis. Those applications are coded in Verilog-A and by using different abstraction levels, the indications of the degree of detail specified on how the function is to be implemented are obtained. Therefore, these behavioral models try to capture as much circuit functionality as possible with far less implementation details than the device-level description of the electronic circuit. Several circuit simulations applying H-Spice simulator are presented to demonstrate the usefulness of the proposed models. In this manner, behavioral modeling can be a possible solution for the successful development of robust chaos-based applications due to various types of systems that can be represented and simulated by means of an abstract model.

Chaotic Planning Paths Generators by Using Performance Surfaces

Chaotic systems have been widely used as path planning generators in autonomous mobile robots due to the unpredictability of the generated trajectories and the coverage rate of the robots workplace. In order to obtain a chaotic mobile robot, the chaotic signals are used to generate True RNGs (TRNGs), which, as is known, exploit the nondeterministic nature of chaotic controllers. Then, the bits obtained from TRNGs can be continuously mapped to coordinates (\(x_n, y_n\)) for positioning the robot on the terrain. A frequent technique to obtain a chaotic bitstream is to sample analog chaotic signals by using thresholds. However, the performance of chaotic path planning is a function of optimal values for those levels. In this framework, several chaotic systems which are used to obtain TRNGs but by computing a quasi-optimal performance surface for the thresholds is presented. The proposed study is based on sweeping the Poincare sections to find quasi-optimal values for thresholds where the coverage rate is higher than those obtained by using the equilibrium points as reference values. Various scenarios are evaluated. First, two scroll chaotic systems such as Chua’s circuit, saturated function, and Lorenz are used as entropy sources to obtain TRNGS by using its computed performance surface. Afterwards, n-scrolls chaotic systems are evaluated to get chaotic bitstreams with the analyzed performance surface. Another scenario is dedicated to find the performance surface of hybrid chaotic systems, which are composed by three chaotic systems where one chaotic system determines which one of the remaining chaotic signals will be used to obtain the chaotic bitstream. Additionally, TRNGs from two chaotic systems with optimized Lyapunov exponents are studied. Several numerical simulations to compute diverse metrics such as coverage rate against planned points, robot’s trajectory evolution, covered terrain, and color map are carried out to analyze the resulting TRNGs. This investigation will enable to increase several applications of TRNGs by considering the proposed performance surfaces.

Optical Response in Subwavelength Optical Fibers with Nanostructured Materials

The optical response of subwavelength fiber under the influence of nanostructured materials when interacting with evanescent field was studied, the results obtained show that there spectral shift to the far infrared.

Design and Fabrication of Subwavelength Optical Fiber

A model of subwavelength optical fibers design is revised through numeric approach. The subwavelength optical fibers have been fabricated by a mechatronic system that implemented of technique flame-brushing for photonic.