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In this paper, the stabilization and high efficiency of an unstable Second Harmonic Generation (SHG) of a Nd : YVO4 laser with a KTP intracavity is carried out by using a passive Q-switching crystal and a parametric modulation method (harmonic modulation) is shown. The harmonic modulation was defined as um(t) = Amsin(2π fmt), with modulation amplitude as Am(Vpp), and modulation frequency as fm(Hz), applied to the pumping of the Nd : YVO4 -KTP laser to control the amplitude and frequency of the emission, thus stabilizing the dynamic states of this laser. The promising application of this green light source is materialized when such light is necessary for high-density optics, such as in the treatment materials industry or in some aesthetic applications.

Considering that chaotic systems are immersed in multiple areas of science and nature and that their dynamics are governed by a great sensitivity to the initial conditions and variations in their parameters, it is of great interest for the scientific community to have tools to characterize and reproduce these trajectories. Two dynamic chaotic systems whose equations are based on the jerky system are used as benchmarks, i.e., the Memristive Shaking Chaotic System (MSCS) and the Unstable Dissipative System of type I (UDSI). One characteristic common to them is their simple mathematical structure and the complexity of their solutions. Therefore, this paper presents a strategy for identifying chaotic trajectories using a recurrent wavelet first-order neural network (RWFONN) that is trained online with an error filtering algorithm and considering the Morlet-wavelet as an activation function. The parameters of the network are adjusted considering the Euclidean distance between the solutions. Finally, the results depict proper identification of the chaotic systems studied through analysis and numerical simulation to validate the behavior and functionality of the proposed network.

In this paper, we present a study of the diffusion properties of a deterministic model for settling particles in two displacement dimensions. The particularities of the novel deterministic model include the generation of Brownian motion and a two-dimensional displacement model without stochastic processes, which are governed by a set of six differential equations. This model is a piecewise system consisting of subsystems governed by jerk equations. With this model, we can consider different conditions of diffusion in both the dimensions and size of the space where the particles are dispersed. The settling time versus the dispersion medium and its size, as well as the average settling time and its probability distributions, are analyzed. Furthermore, the probability distributions for the settling location are presented for the changes in the diffusion parameters and space size. Finally, the basins of attraction for the settling positions are shown as a function of each dimensional diffusion parameter and for the medium size.

At a time when miniaturization and optimization of resources are in the foreground, the development of devices that can perform various functions is a primary goal of technological development. In this work, the use of an Erbium-Doped Fiber Laser (EDFL) is proposed as a basic system for the generation of an optical logic gate. Taking advantage of the dynamic richness of this type of laser and its use in telecommunication systems, the dynamic response is analyzed when the system is perturbed by a digital signal. The emission response of the system is controlled by the intensity of the digital signal, so that it is possible to obtain different logic operations. The numerical results are in good agreement with the experimental observations. The presented work raises new aspects in the use of chaotic systems as a means of obtaining optical logic gates.

During the past years, the study of optical injection has been intensely carried in theoretical and experimental realizations, showing interesting emergent behaviors, and synchronized states between other results. This work proposes an experimental scheme of an array of three driven erbium-doped fiber lasers (EDFLs), which dynamics exhibit the coexistence of multiple attractors. The laser array is controlled by a driver EDFL by injecting its optical intensity into the three coupled driven EDFLs array. The experimental realization was with the aim to induce an attractor tracking in the driving lasers, then to get coexisting states with increasing output power, and to study other emergent behavior given by the differences between doped fibers. To find the multistability regions, some bifurcation diagrams of the laser peak intensities are constructed. The obtained results are identified by comparing them with the modulation frequency. In some cases, the obtained results show that the intensity of the optical output signal of the driven systems is increased with respect to the initial individual response. In the case of synchronized states, it’s possible to get an increased signal from the whole system. The obtained results could have important applications in repeaters of communications systems.

In this paper, the classical Lorenz model is under investigation, in which a periodic heating term replaces the constant one. Applying the variable heating term causes time-dependent behaviors in the Lorenz model. The time series produced by this model are chaotic; however, they have fixed point or periodic-like qualities in some time intervals. The energy dissipation and equilibrium points are examined comprehensively. This modified Lorenz system can demonstrate multiple kinds of coexisting attractors by changing its initial conditions and, thus, is a multi-stable system. Because of multi-stability, the bifurcation diagrams are plotted with three different methods, and the dynamical analysis is completed by studying the Lyapunov exponents and Kaplan-Yorke dimension diagrams. Also, the attraction basin of the modified system is investigated, which approves the appearance of coexisting attractors in this system.

In this paper, the stabilization and high efficiency of an unstable Second Harmonic Generation (SHG) of an Nd:YVO4 laser with a KTP intracavity is demonstrated. By using a passive Q-switching crystal (Cr4+:YAG) and a parametric modulation method (harmonic modulation), the stabilization of the laser is reached. An harmonic modulation was applied to the pumping of the Nd:YVO4-KTP laser to control the amplitude and frequency of the laser emission. The results were characterized by using power spectra analysis, optical spectrum, bifurcation diagrams, and temporal series of the laser intensity. The promising application of this green light source is materialized when such light is necessary for high-density optics, such as in the treatment materials industry or in some aesthetic applications.

In this article, the methods for obtaining time series from an erbium-doped fiber laser (EDFL) and its numerical simulation are described. In addition, the nature of the obtained files, the meaning of the changing file names, and the ways of accessing these files are described in detail. The response of the laser emission is controlled by the intensity of a digital signal added to the modulation, which allows for various logical operations. The numerical results are in good agreement with experimental observations. The authors provide all of the time series from an experimental implementation where various logic gates are obtained.

Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully deterministic set of differential equations. The dynamics of the electronic circuit are characterized using four well-known metrics of Brownian motion, namely: (i) Detrended Fluctuation Analysis (DFA), (ii) power law in the power spectrum, (iii) normal probability distribution, and (iv) Mean Square Displacement (MSD); where traditional Brownian motion exhibits linear time growth of the MSD, a Gaussian distribution, a −2 power law of the frequency spectrum, and DFA values close to 1.5. The obtained results show that for a certain combination of values in the deterministic model, the dynamics in the electronic circuit are consistent with the expectations for a stochastic Brownian behavior. The presented electronic circuit improves the study of Brownian behavior by eliminating the stochastic component, allowing reproducibility of the results through fully deterministic equations, and enabling the generation of physical signals (analog electronic signals) with Brownian-like properties with potential applications in fields such as medicine, economics, genetics, and communications, to name a few.

In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use sliding modes control to synchronize perturbed chaotic systems. We will use two Piecewise Rossler systems unidirectionally coupled, the first like a master and the other like a perturbed slave. The proposed controller is able to synchronize disturbed chaotic systems, even with elimination of chattering problem. Some simulations are presented.

"This thesis presents experimental results on stochastic and deterministic dynamics studies carried out in an Erbium doped fiber lasers (EDFL) which are presented to be compared with the results of numerical simulation using an advanced two-level laser model. The dynamics of this laser under external modulation is very rich; it can exhibit different bifurcations, chaos, and crises; furthermore, for different modulation parameters, one can encounter the coexistence of multiple periodic regimes (attractors). In the experiments with EDFL we demonstrate a strong noise amplification in the vicinity of the critical points. Many are the situations in nature where this phenomenon can be experienced: heart strokes, eruptions, earthquakes, etc. Another phenomenon studied in this thesis is the attractor hopping. As the noise added to a system is increased, the laser brings out different periodic states defining multistability zones. Then, as noise is augmented, more and more of these states come to form part of the hopping attractor. For certain input noise, when more and more states are involved in the hopping process, there is a little change in the output noise. Such a noise-independent regime can be promising for some important applications, in particular, detectors transparent to noise."