Guillermo Huerta Cuellar recibió el grado de Maestro en Ciencias Aplicadas (Fotónica) en el Instituto de Investigación en Comunicaciones Ópticas (IICO), de la Universidad Autónoma de San Luis Potosí, San Luis Potosí en 2004. Posteriormente, obtuvo un título de Doctorado en Ciencias (Óptica) por el Centro de Investigaciones en Óptica (CIO), León Guanajuato, México, en 2009. Desde 2010 hasta la actualidad, ha estado trabajando en el Departamento de Ciencias Exactas y Tecnología en el Centro Universitario de los Lagos, Universidad de Guadalajara. Ha sido Investigador Visitante en el departamento de Matemáticas Aplicadas en el Instituto Potosino de Investigación Científica y Tecnológica, San Luis Potosí, México (2012-2014), en el Departamento de Teoría de Oscilaciones y Control Automático, Facultad de Radiófisica, Universidad Estatal de Lobachevsky de Nizhny Novgorod, Rusia (2016), estancia sabática en el Departamento de Física y Ciencias Ambientales en la Universidad de St. Mary's, San A
EDUCATION
Doctor en Ciencias (Óptica) con linea en dinámica de láseres.
RESEARCH, TEACHING, or OTHER INTERESTS
Earth and Planetary Sciences, Computational Mechanics, Applied Mathematics, Statistical and Nonlinear Physics
The Shape of Chaos: A Geometric Perspective on Characterizing Chaos José Luis Echenausía-Monroy, Luis Javier Ontañón-García, Daniel Alejandro Magallón-García, Guillermo Huerta-Cuellar, Hector Eduardo Gilardi-Velázquez, et al. Mathematics, 2026 Chaotic dynamical systems are ubiquitous in nature and modern technology, with applications ranging from secure communications and cryptography to the design of chaos-based sensors and modeling biological phenomena such as arrhythmias and neuronal behavior. Given their complexity, precise analysis of these systems is crucial for both theoretical understanding and practical implementation. The characterization of chaotic dynamical systems typically relies on conventional measures such as Lyapunov exponents and fractal dimensions. While these metrics are fundamental for describing dynamical behavior, they are often computationally expensive and may fail to capture subtle changes in the overall geometry of the attractor, limiting comparisons between systems with topologically similar structures and similar values in common chaos metrics such as the Lyapunov exponent. To address this limitation, this work proposes a geometric framework that treats chaotic attractors as spatial objects, using topological tools—specifically the α-sphere—to quantify their shape and spatial extent. The proposed method was validated using Chua’s system (including two reported variations), the Rössler system (standard and piecewise-linear), and a fractional-order multi-scroll system. A parametric characterization of the Rössler system was also performed by varying parameter b. Experimental results show that this geometric approach successfully distinguishes between attractors where classical metrics reveal no perceptible differences, in addition to being computationally simpler. Notably, we observed geometric variations of up to 80% among attractors with similar dynamics and introduced a specific index to quantify these global discrepancies. Although this geometric analysis serves as a complement rather than a substitute for chaos detection, it provides a reliable and interpretable metric for differentiating systems and selecting attractors based on their spatial properties.
Real-Time Observer and Neuronal Identification of an Erbium-Doped Fiber Laser Daniel Alejandro Magallón-García, Didier López-Mancilla, Rider Jaimes-Reátegui, Juan Hugo García-López, Guillermo Huerta-Cuellar, et al. Photonics, 2025 This paper presents the implementation of a real-time nonlinear state observer applied to an erbium-doped fiber laser system. The observer is designed to estimate population inversion, a state variable that cannot be measured directly due to the physical limitations of measurement devices. Taking advantage of the fact that the laser intensity can be measured in real time, an observer was developed to reconstruct the dynamics of population inversion from this measurable variable. To validate and strengthen the estimate obtained by the observer, a Recurrent Wavelet First-Order Neural Network (RWFONN) was implemented and trained to identify both state variables: the laser intensity and the population inversion. This network efficiently captures the system’s nonlinear dynamic properties and complements the observer’s performance. Two metrics were applied to evaluate the accuracy and reliability of the results: the Euclidean distance and the mean square error (MSE), both of which confirm the consistency between the estimated and expected values. The ultimate goal of this research is to develop a neural control architecture that combines the estimation capabilities of state observers with the generalization and modeling power of artificial neural networks. This hybrid approach opens up the possibility of developing more robust and adaptive control systems for highly dynamic, complex laser systems.
Topological data analysis approach to time series and shape analysis of dynamical system W. Hussain Shah, S. Rafia Fatima, G. Huerta-Cuellar, J. H. García-López, C. G. Mata Ramirez, et al. Chaos, 2025 In a dynamical system, the time series and phase space play vital roles, and we applied topological data analysis to these characteristics. More precisely, we consider the well-known Rössler-like attractor to analyze time-series and phase-space images. We studied persistent homology representations directly from the time series of the system to obtain point cloud data. In our approach, we converted the time series to a point cloud and computed homology using the Rips complex. This enabled us to measure the topological features of the system behavior. We also applied cubical homology to phase-space images for the first time, a novel contribution that represents an image-based approach to analyze phase portraits. This article provides a review of the topological data analysis of time series using examples with the Python function. Finally, we computed topological machine learning features, such as persistent landscapes, persistence images, and Betti curves. These features enable the automated analysis and classification of dynamical behaviors and, hence, connect topological data analysis with machine learning. This study is new in that it presents a comprehensive topological data analysis pipeline tailored to dynamical systems. The goal is to make these approaches accessible and usable for nonlinear dynamics to analyze their temporal series and phase portraits.
Logic Gate Generation in a Monostable Optical System: Improving the Erbium-Doped Fiber Laser Reconfigurable Logic Operation Samuel Mardoqueo Afanador-Delgado, José Luis Echenausía-Monroy, Guillermo Huerta-Cuellar, Juan Hugo García-López, Erick Emiliano Lopez-Muñoz, et al. Photonics, 2024 A logic gate is typically an electronic device with a Boolean or other type of function, e.g., adding or subtracting, including or excluding according to its logical properties. They can be used in electronic, electrical, mechanical, hydraulic, and pneumatic technology. This paper presents a new method for generating logic gates based on optical systems with an emission frequency equal to that used in current telecommunications systems. It uses an erbium-doped fiber laser in its monostable operating region, in contrast to most results published in the literature, where multistable behavior is required to induce dynamic changes, and where a DC voltage signal in the laser pump current provides the control between obtaining the different logic operations. The proposed methodology facilitates the generation of the gates, since it does not require taking the optical system to critical power levels that could damage the components. It is based on using the same elements that the EDFL requires to operate. The result is a system capable of generating up to five stable and robust logic gates to disturbances validated in numerical simulation and experimental setup. This eliminates the sensitivity to the initial conditions affecting the possible logic gates generated by the system and the need to add noise to the system (as is performed in works based on stochastic logic resonance). The experimental observations confirm the numerical results and open up new aspects of using chaotic systems to generate optical logic gates without bistable states.
Optical Energy Increasing in a Synchronized Motif-Ring Array of Autonomous Erbium-Doped Fiber Lasers José Octavio Esqueda de la Torre, Juan Hugo García-López, Rider Jaimes-Reátegui, José Luis Echenausía-Monroy, Eric Emiliano López-Muñoz, et al. Quantum Beam Science, 2024 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.
Experimental State Observer of the Population Inversion of a Multistable Erbium-Doped Fiber Laser Daniel Alejandro Magallón-García, Didier López-Mancilla, Rider Jaimes-Reátegui, Juan Hugo García-López, Guillermo Huerta Cuellar, et al. Photonics, 2024 In this work, numerical and experimental implementation of a state observer applied to an erbium-doped fiber laser (EDFL) has been developed. The state observer is designed through the mathematical model of the EDFL to estimate the non-measurable variable; however, in numerical estimation, the state variables can be measurable given the mathematical model. Only the laser intensity variable was experimentally measured. The state observer estimated the population inversion through the obtained experimental laser intensity time series fitted with their numerical laser intensity using the mean square error (MSE) tool. A bifurcation diagram of the population inversion time series local maximum was built from the state observer. The state space of the experimental laser intensity versus observed population inversion was built.
Study of multistable visual perception by stochastic modulation using a synergetic model Cybernetics and Physics, 2017
Error-feedback control of multistability R. Sevilla-Escoboza, G. Huerta-Cuellar, R. Jaimes-Reátegui, J.H. García-López, C.I. Medel-Ruiz, et al. Journal of the Franklin Institute, 2017
Selective monostability in multi-stable systems R. Sevilla-Escoboza, A. N. Pisarchik, R. Jaimes-Reátegui, G. Huerta-Cuellar Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences, 2015
Laser synapse Alexander N. Pisarchik, Ricardo Sevilla-Escoboza, Rider Jaimes-Reátegui, Guillermo Huerta-Cuellar, Victor B. Kazantsev Communications in Computer and Information Science, 2014
Synchronization attack to chaotic communication systems Massimiliano Zanin, J. Ricardo Sevilla-Escoboza, Rider Jaimes-Reátegui, J. Hugo Garcıa-Lopez, Guillermo Huerta-Cuellar, et al. Discontinuity Nonlinearity and Complexity, 2013
Rogue waves in a multistable system Alexander N. Pisarchik, Rider Jaimes-Reátegui, Ricardo Sevilla-Escoboza, G. Huerta-Cuellar, Majid Taki Physical Review Letters, 2011
Prebifurcation noise amplification in a fiber laser G. Huerta-Cuellar, A. N. Pisarchik, A. V. Kir’yanov, Yu. O. Barmenkov, J. del Valle Hernández Physical Review E Statistical Nonlinear and Soft Matter Physics, 2009
Emergent behavior in dynamically coupled oscillators and its application in detecting exogenous signals JAV Torres, JJ Barba-Franco, R Jaimes-Reátegui, G Huerta-Cuellar, ... Chaos, Solitons & Fractals 202, 117608 , 2026 2026 Citations: 1
The Shape of Chaos: A Geometric Perspective on Characterizing Chaos JL Echenausía-Monroy, LJ Ontañón-García, DA Magallón-García, ... Mathematics 14 (1), 15 , 2025 2025 Citations: 1
Journal of Dynamical Systems and Complexity An international journal of AMESDYC: The Relevance of Nonlinear Dynamical Systems and Complexity in Science and Technology EC Cantón, ET Cuautle, GH Cuellar Journal of Dynamical Systems and Complexity 1 (1), 1-11 , 2025 2025 Citations: 1
5th Meeting for the Dissemination and Research in the Study of Complex Systems and their Applications E Tlelo-Cuautle, E Campos-Cantón, JM Muñoz-Pacheco, ... Integration, 102562 , 2025 2025
Real-Time Observer and Neuronal Identification of an Erbium-Doped Fiber Laser DA Magallón-García, D López-Mancilla, R Jaimes-Reátegui, ... Photonics 12 (10), 955 , 2025 2025
Complex Systems and Their Applications: Fifth International Conference (EDIESCA 2024) E Tlelo-Cuautle, E Campos-Canton, HE Gilardi-Velazquez, ... Springer Nature , 2025 2025 Citations: 1
Stochastic cloning of dynamical systems with hidden variables AV Andreev, AN Pisarchik, N Kulagin, R Jaimes-Reátegui, ... Physical Review E 112 (1), 015303 , 2025 2025 Citations: 7
Topological data analysis approach to time series and shape analysis of dynamical system W Hussain Shah, S Rafia Fatima, G Huerta-Cuellar, JH García-López, ... Chaos: An Interdisciplinary Journal of Nonlinear Science 35 (6) , 2025 2025 Citations: 7
Persistent homology approach for uncovering transitions to chaos WH Shah, R Jaimes-Reátegui, G Huerta-Cuellar, JH García-López, ... Chaos, Solitons & Fractals 192, 116054 , 2025 2025 Citations: 6
Logic gate generation in a monostable optical system: Improving the erbium-doped fiber laser reconfigurable logic operation SM Afanador-Delgado, JL Echenausía-Monroy, G Huerta-Cuellar, ... Photonics 11 (12), 1103 , 2024 2024 Citations: 2
Optical energy increasing in a synchronized motif-ring array of autonomous erbium-doped fiber lasers JO Esqueda de la Torre, JH García-López, R Jaimes-Reátegui, ... Quantum Beam Science 8 (4), 27 , 2024 2024 Citations: 2
Amplification of Optical Power in the Array of Erbium-Doped Fiber Lasers by Controlling Multistability. Evaluation Using the SCAMPER Method for Innovation Projects CE Rivera-Orozco, MR Ramírez-Jiménez, JH García-López, ... Study of Complex Systems and their Applications Conference, 67-87 , 2024 2024
Experimental State Observer of the Population Inversion of a Multistable Erbium-Doped Fiber Laser DA Magallón-García, D López-Mancilla, R Jaimes-Reátegui, ... Photonics 11 (10), 951 , 2024 2024 Citations: 1
Hidden attractors in chaotic systems with nonlinear functions HM Zeeshan, R Jaimes-reategui, JHG López, S Bibi, G Huerta-cuellar Chaos Theory and Applications 6 (2), 144-151 , 2024 2024 Citations: 4
Opposition to Synchronization of Bistable State in Motif Configuration of Rössler Chaotic Oscillator Systems JHG López, R Jaimes-reategui, G Huerta-cuellar, DL Mancılla Chaos Theory and Applications 6 (2), 131-143 , 2024 2024
Electron Microscopes, Spectroscopy and Their Applications GH Cuellar BoD–Books on Demand , 2024 2024 Citations: 1
Introductory Chapter: Materials Analysis by Using Electronic Microscopes and Spectroscopy GH Cuellar Electron Microscopes, Spectroscopy and Their Applications , 2024 2024
Real-time neural identification using a recurrent wavelet first-order neural network of a chaotic system implemented in an FPAA DA Magallón-García, JH García-López, G Huerta-Cuéllar, ... Integration 96, 102134 , 2024 2024 Citations: 10
Mathematical modeling and optimization for real life phenomena CJ Silva, M Chyba, G Huerta Cuellar Frontiers in Applied Mathematics and Statistics 10, 1389061 , 2024 2024 Citations: 6
Harnessing Multistability: A Novel Approach to Optical Logic Gate Construction Using Erbium-Doped Fiber Lasers S Bibi, G Huerta-Cuellar, JL Echenausía-Monroy, R Jaimes-Reátegui, ... Photonics 11 (2), 176 , 2024 2024 Citations: 1
MOST CITED SCHOLAR PUBLICATIONS
Rogue waves in a multistable system AN Pisarchik, R Jaimes-Reátegui, R Sevilla-Escoboza, G Huerta-Cuellar, ... Physical Review Letters 107 (27), 274101 , 2011 2011 Citations: 259
Synchronization in weighted scale-free networks with degree–degree correlation F Sorrentino, M di Bernardo, GH Cuellar, S Boccaletti Physica D: nonlinear phenomena 224 (1-2), 123-129 , 2006 2006 Citations: 88
Secure chaotic communication based on extreme multistability AN Pisarchik, R Jaimes-Reátegui, C Rodríguez-Flores, JH García-López, ... Journal of the Franklin Institute 358 (4), 2561-2575 , 2021 2021 Citations: 79
Experimental characterization of hopping dynamics in a multistable fiber laser G Huerta-Cuellar, AN Pisarchik, YO Barmenkov Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 78 (3 … , 2008 2008 Citations: 71
Multistate intermittency and extreme pulses in a fiber laser AN Pisarchik, R Jaimes-Reátegui, R Sevilla-Escoboza, G Huerta-Cuellar Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 86 (5 … , 2012 2012 Citations: 69
An approach to generate deterministic Brownian motion G Huerta-Cuéllar, E Jiménez-López, E Campos-Cantón, AN Pisarchik Communications in Nonlinear Science and Numerical Simulation 19 (8), 2740-2746 , 2014 2014 Citations: 66
Generalized synchronization in relay systems with instantaneous coupling R. Gutiérrez, R. Sevilla-Escoboza, P. Piedrahita, C. Finke, U. Feudel, J. M ... Physical Review E 88 (5), 052908 , 2013 2013 Citations: 50
Prebifurcation noise amplification in a fiber laser G Huerta-Cuellar, AN Pisarchik, AV Kir’yanov, YO Barmenkov, ... Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 79 (3 … , 2009 2009 Citations: 43
Multistability emergence through fractional-order-derivatives in a PWL multi-scroll system JL Echenausía-Monroy, G Huerta-Cuellar, R Jaimes-Reátegui, ... Electronics 9 (6), 880 , 2020 2020 Citations: 38
A physical interpretation of fractional-order-derivatives in a jerk system: Electronic approach JL Echenausía-Monroy, HE Gilardi-Velázquez, R Jaimes-Reátegui, ... Communications in Nonlinear Science and Numerical Simulation 90, 105413 , 2020 2020 Citations: 35
Enhancing the stability of the synchronization of multivariable coupled oscillators R Sevilla-Escoboza, R Gutierrez, G Huerta-Cuellar, S Boccaletti, ... arXiv preprint arXiv:1508.06887 , 2015 2015 Citations: 33
Selective monostability in multi-stable systems R Sevilla-Escoboza, AN Pisarchik, R Jaimes-Reátegui, G Huerta-Cuellar Proceedings of the Royal Society A: Mathematical, Physical and Engineering … , 2015 2015 Citations: 29
A novel approach to generate attractors with a high number of scrolls JL Echenausía-Monroy, G Huerta-Cuellar Nonlinear Analysis: Hybrid Systems 35, 100822 , 2020 2020 Citations: 28
Multistability route in a PWL multi-scroll system through fractional-order derivatives JL Echenausía-Monroy, HE Gilardi-Velázquez, N Wang, ... Chaos, Solitons & Fractals 161, 112355 , 2022 2022 Citations: 23
Experimental implementation of a biometric laser synaptic sensor AN Pisarchik, R Sevilla-Escoboza, R Jaimes-Reátegui, G Huerta-Cuellar, ... Sensors 13 (12), 17322-17331 , 2013 2013 Citations: 21
Parametric control for multiscroll generation: Electronic implementation and equilibrium analysis JL Echenausía-Monroy, JH García-López, R Jaimes-Reátegui, ... Nonlinear Analysis: Hybrid Systems 38, 100929 , 2020 2020 Citations: 20
Family of bistable attractors contained in an unstable dissipative switching system associated to a SNLF JL Echenausía-Monroy, JH García-López, R Jaimes-Reátegui, ... Complexity 2018 (6794791), 9 , 2018 2018 Citations: 20
Error-feedback control of multistability R Sevilla-Escoboza, G Huerta-Cuéllar, R Jaimes-Reátegui, ... Journal of the Franklin Institute 354 (16), 7346-7358 , 2017 2017 Citations: 19
Synchronization attack to chaotic communication systems M Zanin, AN Pisarchik, JR Sevilla-Escoboza, R Jaimes-Reátegui, ... Discontinuity, Nonlinearity, and Complexity 2 (4), 333-343 , 2013 2013 Citations: 19
Recent development in optoelectronic devices R Srivastava BoD–Books on Demand , 2018 2018 Citations: 18