Víctor F. Breña-Medina

• Peer-review Journal Papers
  1. Villar-Sepúlveda E., Aguirre P. & Breña-Medina V. (2023). A case study of multiple wave solutions in a reaction-diffusion system using invariant manifolds and global bifurcations, SIAM Journal on Applied Dynamical Systems 22(2), pp. 918-950.
     [arXiv][DOI]
  2. Pantoja-Hernández J., Breña-Medina V. & Santillán M. (2021). Hybrid reaction-diffusion and clock-and-wavefront model for the arrest of oscillations in the somitogenesis segmentation clock, Chaos: An Interdisciplinary Journal of Nonlinear Science, 31(6), 063107. Editor's pick.
     [arXiv][bioRxiv][DOI][Scilight]
  3. Champneys A., Al Saadi F., Breña-Medina V., Grieneisen V., Maree S., Wuyts B. & Verschueren van Rees N. (2021). Bistability, wave pinning and localisation in natural reaction-diffusion systems, Physica D: Nonlinear Phenomena 416, 132735.
     [DOI]
  4. Quiroz-Juárez M. A., Jiménez–Ramírez O., Vázquez-Medina R., Breña-Medina V., Aragón J. L. & Barrio R. A. (2019). Generation of ECG signals from a reaction-diffusion model spatially discretized, Scientific Reports 9 19000.
     [DOI]
  5. Avitabile D., Breña-Medina V. & Ward M. (2018). Spot dynamics in a reaction-diffusion model of plant root hair initiation, SIAM Journal on Applied Mathematics 78(1), pp. 291-319.
     [arXiv][bioRxiv][DOI]
  6. Moctezuma J.C., Breña-Medina V., Nunez-Yanez J. L., & McGeehan J.P. (2016). Neuron Dynamics of Single-Compartment Traub Model for Hardware Implementations , Int. J. Comp. Inf. Eng. 8(7), pp. 1281-1284.
  7. Breña-Medina V., Avitabile D., Champneys A. & Ward M. (2015). Stripe to spot in a plant root hair initiation model, SIAM Journal on Applied Mathematics 75(3), pp. 1090-1119.
     [arXiv][DOI]
  8. Breña-Medina V. & Champneys A. (2014). Subcritical Turing bifurcation and the morphogenesis of localized patterns. Physical Review E 90, 032923.
     [preprint][DOI]
  9. Breña-Medina V., Champneys A., Grierson C. & Ward M. (2014). Mathematical modelling of plant root hair initiation; dynamics of localized
     patches, SIAM Journal on Applied Dynamical Systems 13(1), pp. 210-248.
     [preprint][DOI]
  10. Sánchez-Garduño F. & Breña-Medina V. (2010). Searching for Spatial Patterns in a Pollinator-Plant-Herbivore Mathematical Model, Bulletin of Mathematical Biology 73(5), pp. 1118-1153.
      [PDF][DOI]
  11. Sánchez-Garduño F. & Breña-Medina V. (2008). Spatiotemporal dynamics of a three interacting species mathematical model inspired in physics, AIP Conf. Pro. 978, pp. 115-184. (Conference proceedings).
• Outreach Essays
  1. Breña-Medina V. (2023). Sincronización y naturaleza, Mundo ITAM (febrero), Instituto Tecnológico Autónomo de México (written in Spanish).
     [Liga]
  2. Breña-Medina V. (2018). De cuando la existencia y la unicidad van de la mano; elucubraciones de un 'dinamiquero', Laberintos e Infinitos 47(autumn), Departamento Académico de Matemáticas, Instituto Tecnológico Autónomo de México, pp. 6-14 (written in Spanish).
     [Liga]
  3. Breña-Medina V. (2018). La discreción dinámica de una población y sus recursos, Motivos Matemáticos 1(2), Departamento de Matemáticas, Universidad Nacional Autónoma de México, Artículos de matemáticas aplicadas (written in Spanish).
     [Link]
  4. Breña-Medina V. (2016). Caos: ¿un orden para el desorden?, SAHUARUS, Revista Electrónica de Matemáticas 1(2), Departamento de Matemáticas, Universidad de Sonora, pp. 1-18 (written in Spanish).
     [DOI]
  5. Breña-Medina V. (2015). Biología y Matemáticas; Alan Turing, sus patrones y otras monerías, Boletín de la UNAM Campus Morelia, 58 (written in Spanish).
     [Link]
  6. Breña-Medina V. (2015). ¿Es cierto que el sistema circulatorio y los copos de nieve se parecen más de lo que uno pensaría?, Boletín de la UNAM Campus Morelia, pp. 8 (written in Spanish).
  7. Breña-Medina V. (2015). Biología y Matemáticas; Alan Turing, sus patrones y otras monerías, Boletín de la UNAM Campus Morelia, 58, pp. 1 (written in Spanish).
     [Link]
• Book Chapters
  1. Breña-Medina V. Dynamical Features of a Biochemical Interaction in a Plant Root Hair Cell. Olivares-Quiroz L., Resendis-Antonio O. (eds) Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues. Springer, Cham, 2018, pp. 189-215.
     [DOI]
  2. Breña-Medina V. Reacción-Difusión y estructuras localizadas en la naturaleza. Tópicos Selectos de Matemáticas: Aportaciones en Matemáticas 1. Tlaxcala, México: Universidad Autónoma de Tlaxcala, 2016, pp. 97-114 (written in Spanish).

• Courses: Spring 2024 (in Spanish)
  • Cálculo Diferencial e Integral II (avisos y temario).
  • Laboratorios del curso.
    
• Teaching notes (in Spanish).
  • Teorema de existencia y unicidad (EDO).
  • Método de Duhamel para sistemas de EDO.
  • Método de Duhamel y coeficientes indeterminados.
  • EDO exactas.
  • Ejercicio: regla de la cadena.
  • Ejercicio: optimización Karush-Kuhn-Tucker.
  • Teorema de existencia y unicidad (EDO).
• PhD project (Posgrado en Ciencias Matemáticas, UNAM).
  This project consists of the understanding of localised solutions dynamics in a reaction-hyperbolic diffusion paradigma.
  Interested candidates drop an email to victor.brena@itam.mx and/or to Dr. Ramón Plaza.

• Supervised theses
  1. Santiago Villareal Abraham. Undergraduate, ITAM; Applied Mathematics.
     BSc Thesis (Special Mention): Ecuación de Swift-hohenberg; un estudio de la bifurcación Hamilton-Hopf.
     Degree achievement date: 12/December/2023.
  2. Ana Fernández Baranda. Undergraduate, ITAM; Applied Mathematics.
     BSc Thesis: Algunas propiedades espacio-temporales en un modelo de la interacción entre PU.1 y GATA-1.
     Degree achievement date: 16/August/2021.
  3. Francisco Castañeda Ruan. Undergraduate, ITAM; Applied Mathematics.
     BSc Thesis (Honorable Mention): Modelación matemática de las oscilaciones químicas producidas por la reacción de Belousov-Zhabotinsky.
     Degree achievement date: 16/April/2021.
  4. Edgardo E. Villar Sepúlveda. Posgrado en Ciencias Mención Matemática, UTFSM; Mathematics (co-supervised with Pablo Aguirre).
     MSc Thesis: Difusión espacial en un modelo depredador-presa con efecto Allee fuerte en la presa y respuesta funcional razón-dependiente.
     Degree achievement date: 5/November/2019
  5. Mariana Harris Heredia. Undergraduate, ITAM; Applied Mathematics.
     BSc Thesis (Honorable Mention): Mathematical Modelling of Quorum Sensing Dynamics.
     Degree achievement date: 14/June/2019
  6. Patricia Pérez Sánchez. Undergraduate, UNPA; Applied Mathematics (co-supervised with Beatriz Luna).
     BSc Thesis: Comportamiento dinámico de diferentes modelos matemáticos del Bruselador.
     Degree achievement date: 18/December/2017
  7. Gabriel Adrián Salcedo Varela. Posgrado en Matemáticas, U. of Sonora; Mathematics (co-supervised with Daniel Olmos).
     MSc Thesis: Estudio de la Bifurcación de Turing-Hopf en Sistemas de Reacción-Difusión.
     Degree achievement date: 25/August/2017
  8. Shaday Guerrero Flores. Posgrado Conjunto en Ciencias Matemáticas, UNAM-UMSNH; Mathematics.
     MSc Dissertation: Interacción presa-depredador en sistemas de reacción-difusión.
     Degree achievement date: 15/August/2017
• Theses under current supervision
  1. Angélica Verenice Villavicencio Soriano. Undergraduate, School of Sciences, UNAM; Mathematics.
     BSc Thesis: Un modelo de reacción-difusión para la morfogénesis de los somitas.
     Degree achievement date: thesis in review.
  2. Manuel Hernández Calderón. Undergraduate, ITAM; Applied Mathematics.
  3. Daniela Gómez Guridi. Undergraduate, co-supervised with Elisa Domínguez Hüttinger, ITAM; Applied Mathematics.

• AUTO-07P. A program for continuation and bifurcation analysis on ordinary differential equations, it can do some computations on parabolic partial differential equations, and also includes software HOMCONT for bifurcation analysis of homoclinic orbits. It is well documented, and even though it works the best on Linux, can also perform very nicely on MAC OS X. More details can be found here and in the short course: "Numerical Continuation with AUTO".
• XPPAUT & XPPy. XPPAUT is a software for solving some partial differential equations in 1D, ordinary differential equations (including boundary value problems), differential algebraic equations, difference equations, delay equations, stochastic equations and functional equations, which is well documented and easy to install on Linux, MAC OS X and Windows; AUTO code is included on it as well. Moreover, Jakub Nowacki has created a Python interface called XPPy, which I have found particularly quite advantageous.
• Python. This is an object-oriented, high-level programming language that offers wide applicability range. Here are some webpages to libraries I frequently use: matplotlib, sympy, scipy & numpy, and for those who come from Matlab® world, numpy for Matlab users.
  Few simple script examples:
  • Script which numerically solves the Schnackenberg system in 1D by applying the method of lines.
  • Build a simple 2D surface.
  • Compute dispersion relation of a nonlinear nonlocal eigenvalue problem for an interior homoclinic stripe under transverse small perturbations; script.
  • Compute a nonlinear PDE system in 1D using XPPAUT via XPPy, and build figures to finally encode them altogether into a movie; then play it on an endless loop; script.
  • Load a inhomogeneously distributed data file of a 2×2 system, interpolate it homogeneously, and save output data on an intercalary way in a single XPPAUT format file or separately. It can be run in AUTO interface; script.
• Overleaf. This is a nice, useful and very well documented on-line LaTex editor. There a growing LaTeX-examples database can be found, which includes a PhD thesis template for the University of Bristol, and a slightly modified figure from my thesis (TikZ package and beamer document class are used).
  Here, you can access an ITAM thesis example, along with valuable tips for writing mathematics documents (in Spanish).
• Miscellaneous.
  • LaTeX templates for letters, articles, books, presentations and posters (oriented to Spanish speakers).
• Colleagues and collaborators.

  Pablo Aguirre José Luis Aragón-Vera Daniele Avitabile Pablo Castañeda Alan Champneys Marisol Flores Alessio Franci Laura Rocío González-Ramírez Claire Grierson Marco A. Herrera

  Bernd Krauskopf Mayra Núñez Daniel Olmos Hinke M. Osinga Pablo Padilla Ramón Plaza Faustino Sánchez-Garduño Moisés Santillán Jorge X. Velasco Michael J. Ward

I was born the Día de Muertos in the Mexico City, this is a national holiday whose essence is gathering family and friends to remember our beloved relatives and friends who have passed away. Contrarily to what would be believed, remembrance is achieved throughout joy more than regret. This celebration is a very interesting mixture of pre-Columbian cultures and the Spanish one, not only oneself can enjoy of the characteristic Mexican colours and scents, product of cultures clash, but also see outstanding adornments in cemeteries made of petals and traditional dishes.

I am strongly keen on travelling to the nearest beautiful landscape I can find. I am also an avid fan of films and music. Also, I have a particular interest in food, so not only cooking is a pleasure for me, but also I am quite fond of hunting for places, either public houses and restaurants, where eating and drinking may be a splendid experience.

I have a weakness for comics though; here are some links that make my mornings time to time: XKCD, SMBC, and Abstruse Goose. I follow comedians as Matt Parker, who definitely knows how to make laughs with maths; here is a great sketch. Also, I practice Brazilian Jiu Jitsu; here is a link to a Roger Gracie clip - probably one of the best competitors in the world.