Gilardi Velázquez, Héctor Eduardo

Main Affiliation

Preferred name

Official Name

Gilardi Velázquez, Héctor Eduardo

ORCID

0000-0002-4978-4526

Researcher ID

AAT-3915-2020

Scopus Author ID

57195627627

Now showing 1 - 10 of 28

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Analysis of Chaotic Systems in the Generation of Random Phases for Amplitude Holograms
(Akif Akgul, 2025-07-31)
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<jats:p xml:lang="en">In recent decades, there has been great interest in the development of applications of chaotic systems in cryptographic systems and communication systems due to their non-periodic and long-term unpredictable nature. In this work, the properties of different chaotic systems, both continuous and discrete in time, are analyzed for the generation of pseudo-random phases practical for holography. The different types of dynamics generated by different systems are analyzed using bifurcation diagrams, transition from chaos to periodic orbits and equilibrium points, as well as two methodologies to construct the phase (Cartesian and polar). Our results shows a better performance in discrete-time systems by generating smooth transitions in the formed patterns and avoiding the generation of artifacts in the holograms, given the wider range of parameters in which the system is stable.</jats:p>
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A comparison study of diffusion properties in Brownian motion models: From the stochastic to discrete and continuous chaotic-based models
(AIP Publishing, 2025-04-01)
P. K. De Nova Ríos
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S. E. Velázquez-Pérez
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E. Campos-Cantón
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<jats:p>The Brownian motion has been studied from different perspectives. Einstein proposed the first mathematical description of the Brownian motion of a free particle in one dimension; later, Langevin proposed another model using stochastic differential equations based on Newton's second law, and recently, deterministic models based on Langevin equations have been proposed, where the fluctuating acceleration is replaced, by the jerk equation and by a discrete system “booster” capable of generating chaos. In this work, we compare the statistical properties of the Brownian motion generated by a chaotic map, the Jerk equation, and the classical Langevin Model under parameter variations. We analyze their properties, such as the mean square displacement, the probability distribution for average displacement, and the type of diffusion generated by these models through the detrended fluctuation analysis and the diffusion coefficient calculation. Our results reveal that deterministic models can serve as viable alternatives to classical stochastic models, offering comparable statistical properties for particle diffusion.</jats:p>
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Analysis and Simulation of Dynamic Heat Transfer and Thermal Distribution in Burns with Multilayer Models Using Finite Volumes
(MDPI AG, 2025-10-01)
Adriana Sofia Rodríguez-Pérez
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Stephanie Esmeralda Velázquez-Pérez
<jats:p>Burns represent a significant medical challenge, and the development of theoretical models has the potential to contribute to the advancement of new diagnostic tools. This study aimed to perform numerical simulations of the Pennes bioheat transfer equation, incorporating heat generation terms due to the body’s immunological response to thermal injury, as well as changes in skin thermal parameters and blood perfusion for each burn type. We propose the incorporation of specific parameters and boundary conditions related to multilayer perfusion into the Pennes bioheat model. Using the proposed layered skin model, we evaluate temperature differences to establish correlations for determining burn depth. In this investigation, 1D and 3D algorithms based on the finite volume method were applied to capture transient and spatial thermal variations, with the resulting temperature distributions demonstrating the ability of the proposed models to describe the expected thermal variations in healthy and burned tissue. This work demonstrates the potential of the finite volume method to approximate the solution of the Pennes biothermal equation. Overall, this study provides a computational framework for analyzing heat transfer in burn injuries and highlights the relevance of mathematical simulations as a tool for future research on infrared thermography in medicine.</jats:p>
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A Comparative Study of Brownian Dynamics Based on the Jerk Equation Against a Stochastic Process Under an External Force Field
(MDPI AG, 2025-02-28)
Adriana Ruiz-Silva
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Bahia Betzavet Cassal-Quiroga
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Rodolfo de Jesus Escalante-Gonzalez
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<jats:p>Brownian motion has been studied since 1827, leading to numerous important advances in many branches of science and to it being studied primarily as a stochastic dynamical system. In this paper, we present a deterministic model for the Brownian motion for a particle in a constant force field based on the Ornstein–Uhlenbeck model. By adding one degree of freedom, the system evolves into three differential equations. This change in the model is based on the Jerk equation with commutation surfaces and is analyzed in three cases: overdamped, critically damped, and underdamped. The dynamics of the proposed model are compared with classical results using a random process with normal distribution, where despite the absence of a stochastic component, the model preserves key Brownian motion characteristics, which are lost in stochastic models, giving a new perspective to the study of particle dynamics under different force fields. This is validated by a linear average square displacement and a Gaussian distribution of particle displacement in all cases. Furthermore, the correlation properties are examined using detrended fluctuation analysis (DFA) for compared cases, which confirms that the model effectively replicates the essential behaviors of Brownian motion that the classic models lose.</jats:p>
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A Transformer-Based Multi-Task Learning Model for Vehicle Traffic Surveillance
(MDPI AG, 2025-11-29)
Fernando Hermosillo-Reynoso
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Erica Ruiz-Ibarra
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Armando García-Berumen
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Vehicle traffic surveillance (VTS) systems are based on the automatic analysis of video sequences to detect, classify, and track vehicles in urban environments. The design of new VTS systems requires computationally efficient architectures with high performance in accuracy. Conventional approaches based on multi-stage pipelines have been successfully used during the last decade. However, these systems need to be improved to face the challenges of complex, high-mobility traffic environments. This article proposes an efficient system based on transformer architectures for VTS channels. The proposed analysis system is evaluated in scenarios with high vehicle density and occlusions. The results demonstrate that the proposed scheme reduces the computational complexity required for multi-object detection and tracking and exhibits a Multiple Object Tracking Accuracy (MOTA) of 0.757 and an identity F1 score (IDF1) of 0.832 when compared to conventional multi-stage systems under the same conditions and parameters, along with achieving a high detection precision of 0.934. The results show the viability of implementing the proposed system in practical applications for high-density vehicle VTS channels.
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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
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Juan Hugo García-López
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Rider Jaimes-Reátegui
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José Luis Echenausía-Monroy
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Eric Emiliano López-Muñoz
<jats:p>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.</jats:p>
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Codification of Images Based on Deterministic Brownian Motion
(2024)
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J. L. Echenausia-Monroy
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R. J. Escalante-González
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Eric Campos
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Emergence of a square chaotic attractor through the collision of heteroclinic orbits
(2020)
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Rodolfo J. Escalante-González
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Eric Campos
Scopus© Citations 6 7 1
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Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System
(2020)
José Luis Echenausía-Monroy
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Guillermo Huerta-Cuellar
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Rider Jaimes-Reátegui
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Juan Hugo García-López
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Vicente Aboites
<jats:p>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.</jats:p>
Scopus© Citations 20 40 2
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Analysis of particle settlement characteristics in a one-dimensional deterministic model
(2025)
S. E. Velázquez-Pérez
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E. Campos-Cantón
<jats:p> 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. </jats:p>
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Gilardi Velázquez, Héctor Eduardo

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