Now showing 1 - 10 of 16
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Optical Energy Increasing in a Synchronized Motif-Ring Array of Autonomous Erbium-Doped Fiber Lasers

2024 , José Octavio Esqueda de la Torre , Juan Hugo García-López , Rider Jaimes-Reátegui , José Luis Echenausía-Monroy , Eric Emiliano López-Muñoz , Gilardi Velázquez, Héctor Eduardo , Guillermo Huerta-Cuellar

This work investigates the enhancement of optical energy in the synchronized dynamics of three erbium-doped fiber lasers (EDFLs) that are diffusively coupled in a unidirectional ring configuration without the need for external pump modulation. Before the system shows stable high-energy pulses, different dynamic behaviors can be observed in the dynamics of the coupled lasers. The evolution of the studied system was analyzed using different techniques for different values of coupling strength. The system shows the well-known dynamic behavior towards chaos at weak coupling, starting with a fixed point at low coupling and passing through Hopf and torus bifurcations as the coupling strength increases. An interesting finding emerged at high coupling strengths, where phase locking occurs between the frequencies of the three lasers of the system. This phase-locking leads to a significant increase in the peak energy of the EDFL pulses, effectively converting the emission into short, high amplitude pulses. With this method, it is possible to significantly increase the peak energy of the laser compared to a continuous EDFL single pulse.

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Beyond Chaos in Fractional-Order Systems: Keen Insight in the Dynamic Effects

2024 , José Luis Echenausía-Monroy , Luis Alberto Quezada-Tellez , Gilardi Velázquez, Héctor Eduardo , Omar Fernando Ruíz Martínez , María del Carmen Heras-Sánchez , Jose E. Lozano-Rizk , José Ricardo Cuesta-García , Luis Alejandro Márquez-Martínez , Raúl Rivera-Rodríguez , Jonatan Pena Ramirez , Joaquín Álvarez

Fractional calculus (or arbitrary order calculus) refers to the integration and derivative operators of an order different than one and was developed in 1695. They have been widely used to study dynamical systems, especially chaotic systems, as the use of arbitrary-order operators broke the milestone of restricting autonomous continuous systems of order three to obtain chaotic behavior and triggered the study of fractional chaotic systems. In this paper, we study the chaotic behavior in fractional systems in more detail and characterize the geometric variations that the dynamics of the system undergo when using arbitrary-order operators by asking the following question: is the Lyapunov exponent sufficient to describe the dynamical variations in a chaotic system of fractional order? By quantifying the convex envelope generated by the 2D projection of the system into all its phase portraits, the changes in the area of the system, as well as the volume of the attractor, are characterized. The results are compared with standard metrics for the study of chaotic systems, such as the Kaplan–Yorke dimension and the fractal dimension, and we also evaluate the frequency fluctuations in the dynamical response. It is found that our methodology can better describe the changes occurring in the systems, while the traditional dimensions are limited to confirming chaotic behaviors; meanwhile, the frequency spectrum hardly changes. The results deepen the study of fractional-order chaotic systems, contribute to understanding the implications and effects observed in the dynamics of the systems, and provide a reference framework for decision-making when using arbitrary-order operators to model dynamical systems.

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Emergent Behaviors in Coupled Multi-scroll Oscillators in Network with Subnetworks

2024 , Adrıana Ruiz-silva , Bahia Betzavet Cassal-quiroga , Eber J. ávila-martínez , Gilardi Velázquez, Héctor Eduardo

This paper presents the emergence of two collective behaviors in interconnected networks. Specifically, the nodes in these networks belong to a particular class of piece-wise linear systems. The global topology of the network is designed in the form of connected subnetworks, which do not necessarily share the same structure and coupling strength. In particular, it is considered that there are two levels of connection, the internal level is related to the connection between the nodes of each subnetwork; while the external level is related to connections between subnetworks. In this configuration, the internal level is considered to provide lower bounds on the coupling strength to ensure internal synchronization of subnetworks. The external level has a relevant value in the type of collective behavior that can be achieved, for which, we determine conditions in the coupling scheme, to achieve partial or complete cluster synchronization, preserving the internal synchronization of each cluster. The analysis of the emergence of stable collective behavior is presented by using Lyapunov functions of the different coupling. The theoretical results are validated by numerical simulations.

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Bidimensional Deterministic Model for Diffusion and Settling of Particles

2023 , Stephanie Esmeralda Velázquez Pérez , Eric Campos-Cantón , Guillermo Huerta Cuellar , Héctor Eduardo Gilardi Velázquez

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.

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Multistability route in a PWL multi-scroll system through fractional-order derivatives

2022 , J.L. Echenausía-Monroy , Gilardi Velázquez, Héctor Eduardo , Ning Wang , R. Jaimes-Reátegui , J.H. García-López , G. Huerta-Cuellar

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Emergence of a square chaotic attractor through the collision of heteroclinic orbits

2020 , Gilardi Velázquez, Héctor Eduardo , Rodolfo J. Escalante-González , Eric Campos

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Time Management of Modes of Operation for Survival of a Satellite Mission: Power Simulation in MATLAB and STK

2021 , Manuel González , Gilardi Velázquez, Héctor Eduardo , Gutiérrez, Sebastián , Ruiz-Martinez, O.F.

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A physical interpretation of fractional-order-derivatives in a jerk system: Electronic approach

2020 , J.L. Echenausía-Monroy , Gilardi Velázquez, Héctor Eduardo , R. Jaimes-Reátegui , V. Aboites , G. Huerta-Cuellar

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Analysis of particle settlement characteristics in a one-dimensional deterministic model

2025 , S. E. Velázquez-Pérez , Gilardi Velázquez, Héctor Eduardo , E. Campos-Cantón

In this paper, we investigate how particles settle in a one-dimensional deterministic model. We leverage a model for deterministic Brownian motion and introduce boundary conditions to simulate particle settling. By adjusting parameters in the Jerk equation, we explore how different diffusion, and the size of the settling space affect the particles’ behavior. We analyze how these parameters influence the settling time and its relationship to the dispersion medium. Additionally, we examine statistical properties as follows: the average settling time, the probability distributions for mean displacement, and how the probability distribution of settling times changes with the size of the space.

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Implementation of the cFS framework for the development of software in aerospace missions: first application in an undergraduate program in Mexico

2021 , M. De la Vega-Martínez , M.C. Velázquez-García , M.F. Zavala-López , Hernandez, Erika , R.A. Gutiérrez-Esparza , D.G. Arcos-Bravo , D. Medina , Gilardi Velázquez, Héctor Eduardo , D. McComas