Gilardi Velázquez, Héctor Eduardo
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Gilardi Velázquez, Héctor Eduardo
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Gilardi Velázquez, Héctor Eduardo
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hgilardi
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ORCID
Scopus Author ID
57195627627
Researcher ID
AAT-3915-2020

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Observaciones ontólogicas al caos determinista como forma del universo

2001 , Gilardi Velázquez, Héctor Eduardo

Este artículo trata de explicar cómo algunos presupuesto de la Teoría del Caos Determinista convertirían la presencia del azar en los procesos naturales en una causa formal del universo. También se compara esta posición con una visión compatible de teleología metafísica.

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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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Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties

2024 , J. L. Echenausía-monroy , Rıcardo Cuesta-garcía , Gilardi Velázquez, Héctor Eduardo , Sishu Shankar Muni , Joaquin Alvarez-gallegos

The study of dynamical systems is based on the solution of differential equations that may exhibit various behaviors, such as fixed points, limit cycles, periodic, quasi-periodic attractors, chaotic behavior, and coexistence of attractors, to name a few. In this paper, we present a simple and novel method for predicting the occurrence of tipping points in a family of Piece-Wise Linear systems (PWL) that exhibit a transition from monostability to multistability with the variation of a single parameter, without the need to compute time series, i.e., without solving the differential equations of the system. The linearized system of the model is analyzed, the stable and unstable manifolds are taken to be real vectors in space, and the changes suffered by these vectors as a result of the modification of the parameter are examined using such simple metrics as the magnitude of a vector or the angle between two vectors in space. The results obtained with the linear analysis of the system agree well with those obtained with the numerical resolution of the dynamical system itself. The work presented here is an extension of previous results on this topic and contributes to the understanding of the mechanisms by which a system changes its stability by fragmenting its basin of attraction. This, in turn, enriches the field by providing an alternative to numerical resolution to identify quantitative changes in the dynamics of complex systems without having to solve the differential equation system.

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Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System

2020 , José Luis Echenausía-Monroy , Guillermo Huerta-Cuellar , Rider Jaimes-Reátegui , Juan Hugo García-López , Vicente Aboites , Cassal Quiroga, Bahia Betzavet , Gilardi Velázquez, Héctor Eduardo

In this paper, the emergence of multistable behavior through the use of fractional-order-derivatives in a Piece-Wise Linear (PWL) multi-scroll generator is presented. Using the integration-order as a bifurcation parameter, the stability in the system is modified in such a form that produces a basin of attraction segmentation, creating many stable states as scrolls are generated in the integer-order system. The results here presented reproduce the same phenomenon reported in systems with integer-order derivatives, where the multistable regimen is obtained through a parameter variation. The multistable behavior reported is also validated through electronic simulation. The presented results are not only applicable in engineering fields, but they also enrich the analysis and the understanding of the implications of using fractional integration orders, boosting the development of further and better studies.

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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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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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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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Generation of Self-Excited, Hidden and Non-Self-Excited Attractors in Piecewise Linear Systems

2023 , Eric Campos Cantón , Rodolfo de Jesús Escalante González , Gilardi Velázquez, Héctor Eduardo

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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

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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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