F. Sanchez-garduno - Academia.edu (original) (raw)

Papers by F. Sanchez-garduno

The Journal of Agricultural Science, 1996

This group, which is concerned with the applications of mathematics to agricultural science, is s... more This group, which is concerned with the applications of mathematics to agricultural science, is sponsored by the Biotechnology and Biological Sciences Research Council. It was formed in 1970, and has since met at approximately yearly intervals in London for one-day meetings. The twenty-eighth meeting of the group, chaired by Dr. D. A. Rose of the Department of Agricultural & Environmental Science, University of Newcastle, was held in the Wellcome Meeting Room at the Royal Society, 6 Carlton House Terrace, London on Friday, 29 March 1996, when the following papers were read. An investigation of the ventilation of a day-old chick transport vehicle. A

SIGLEAvailable from British Library Document Supply Centre- DSC:D177114 / BLDSC - British Library... more SIGLEAvailable from British Library Document Supply Centre- DSC:D177114 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

AIP Conference Proceedings, 2008

Spatio‐temporal dynamics of a three interacting species mathematical model inspired in physics. [... more Spatio‐temporal dynamics of a three interacting species mathematical model inspired in physics. [AIP Conference Proceedings 978, 115 (2008)]. Faustino Sánchez‐ Garduño, Víctor F. Breña‐Medina. Abstract. In this paper we ...

Royal Society Open Science, 2014

Predator–prey relationships are one of the most studied interactions in population ecology. Howev... more Predator–prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species, despite firm field evidence of such phenomena in nature. In this paper, we build a mathematical model capable of reproducing the main phenomenological features of role reversal in a classical system and present results for both the temporal and spatio-temporal cases. We show that, depending on the choice of parameters, our role-reversal dynamical system exhibits excitable-like behaviour, generating waves of species' concentrations that propagate through space. Our findings fill a long-standing gap in modelling ecological interactions and can be applicable to better understanding ecological niche shifts and planning of sustainable ecosystems.

Bulletin of Mathematical Biology, 2011

ICES Journal of Marine Science, 1949

D'arcy Wentworth Thompson (1860-1948) The second day of May 2010 was 150 years since D’Arcy W... more D'arcy Wentworth Thompson (1860-1948) The second day of May 2010 was 150 years since D’Arcy Wentworth Thompson was born. He was a universal man who combined mathematics and biology within a framework of erudite classical knowledge in order to develop lines of thought that can explain the origins and evolution of biological patterns. Unfortunately, this important anniversary went unnoticed for the majority of the scientific community. In this essay, we recall the highlights of his work, stress the relevance and validity of his proposals and pay tribute to a scientist undeservedly forgotten by the mainstream of the current evolutionary school. Key words Morphology, evolution, biomathematics, biophysics, living patterns, structuralism, development biology.

INTERdisciplina

La alometría es el estudio de la variación de las dimensiones anatómicas y fisiológicas en los se... more La alometría es el estudio de la variación de las dimensiones anatómicas y fisiológicas en los seres vivos en tanto se correlacionan; esto permite aproximarse a la comprensión de los organismos como un todo y no como la suma de sus partes. A partir del modelo dinámico del principio de alometría, en este trabajo se presenta la controversia sobre el escalamiento de la tasa metabólica respecto a la masa corporal (entre las leyes de Rubner y de Kleiber), se plantea una nueva argumentación para resolverla en términos de la estructura autosemejante de las redes de transporte e intercambio de material y se reflexiona sobre cómo el entramado alométrico provee un argumento en favor de la evolución biológica mediante cambios múltiples en toda la arquitectura de los organismos y no por la acumulación de pequeños cambios en este o aquel órgano.

Nonlinear Analysis: Real World Applications

Journal of theoretical biology, Jan 25, 2018

This paper deals with the study of spatial and spatio-temporal patterns in the reaction-diffusion... more This paper deals with the study of spatial and spatio-temporal patterns in the reaction-diffusion FitzHugh-Nagumo model on growing curved domains. This is carried out on two exemplar cases: a torus and a sphere. We compute bifurcation boundaries for the homogeneous steady state when the homogeneous system is monostable. We exhibit Turing and Turing-Hopf bifurcations, as well as additional patterning outside of these bifurcation regimes due to the multistability of patterned states. We consider static and growing domains, where the growth is slow, isotropic, and exponential in time, allowing for a simple analytical calculation of these bifurcations in terms of model parameters. Numerical simulations allow us to discuss the role played by the growth and the curvature of the domains on the pattern selection on the torus and the sphere. We demonstrate parameter regimes where the linear theory can successfully predict the kind of pattern (homogeneous and heterogeneous oscillations and st...

Bulletin of Mathematical Biology, 2016

In this paper, we study the emergence of different patterns that are formed on both static and gr... more In this paper, we study the emergence of different patterns that are formed on both static and growing domains and their bifurcation structure. One of these is the so-called Turing-Hopf morphogenetic mechanism. The reactive part we consider is of FitzHugh-Nagumo type. The analysis was carried out on a flat square by considering both fixed and growing domain. In both scenarios, sufficient conditions on the parameter values are given for the formation of specific space-time structures or patterns. A series of numerical solutions of the corresponding initial and boundary value problems are obtained, and a comparison between the resulting patterns on the fixed domain and those arising when the domain grows is established. We emphasize the role of growth of the domain in the selection of patterns. The paper ends by listing some open problems in this area.

In this paper we review the existence of different types of travellingwave solutions u(x; t) = OE... more In this paper we review the existence of different types of travellingwave solutions u(x; t) = OE(x \Gamma ct) of degenerate non-linear reactiondiffusionequations of the form u t = [D(u)u x ] x + g(u) for differentdensity-dependent diffusion coefficients D and kinetic part g. These includethe non-linear degenerate generalized Fisher-KPP and the Nagumoequations. Also, we consider an equation whose diffusion

Boletín de la Sociedad Matemática Mexicana, 2014

ABSTRACT In this paper, we derive and analyze both analytically and numerically a mathematical mo... more ABSTRACT In this paper, we derive and analyze both analytically and numerically a mathematical model for three interacting populations. These take the form of a herbivore, a plant, and a pollinator. The full model is a nonlinear reaction–diffusion–advection system, which is derived on the basis of a series of plausible and widely supported ecological hypothesis. The study we present here deals with the conditions for the coexistence of the three interacting species. The analysis is carried out in two stages. For the homogeneous case, the mathematical model reduces to a nonlinear three-dimensional autonomous ODE system, which, as the ecological parameters change, exhibits different dynamical behaviors, namely a limit cycle and a positive attractor. The non-homogeneous case is studied mainly by means of numerical simulations of the full model defined on a rectangular region and considering appropriate initial and boundary conditions. Our results strongly suggest the stabilizing role played by the herbivore population which, in turn means that the introduction of this population into the mutualistic pollinator–plant interaction, favors the coexistence of the three interacting species.

Experimental and Theoretical Advances in Biological Pattern Formation, 1993

The Scientific World Journal, 2016

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion... more This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (atD(0)=0) and advection-degenerate (ath′(0)=0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection termh(u):(1) h′(u)is constantk,(2) h′(u)=kuwithk>0, and(3)it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, wherek=0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclini...

Discrete Contin Dyn Sys Ser B, 2001

We study a reaction diffusion model recently proposed in to describe the spatiotemporal evolution... more We study a reaction diffusion model recently proposed in to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting mathematical feature of the model, which is a coupled pair of partial differential equations, is that the bacterial density satisfies a degenerate nonlinear diffusion equation. It was shown numerically that this model can exhibit quasi-one-dimensional constant speed travelling wave solutions. We present an analytic study of the existence and uniqueness problem for constant speed travelling wave solutions. We find that such solutions exist only for speeds greater than some threshold speed giving minimum speed waves which have a sharp profile. For speeds greater than this minimum speed the waves are smooth. We also characterise the dependence of the wave profile on the decay of the front of the initial perturbation in bacterial density. An investigation of the partial differential equation problem establishes, via a global existence and uniqueness argument, that these waves are the only long time solutions supported by the problem. Numerical solutions of the partial differential equation problem are presented and they confirm the results of the analysis.

wseas.us

We derive from first principles a general model to describe the spatio-temporal dynamics of two m... more We derive from first principles a general model to describe the spatio-temporal dynamics of two morphogens. The diffusive part of the model incorporates the dynamics, growth and curvature of two-dimensional domains embedded in R 3 . Our generalized diffusion process includes spatio-temporal varying diffusion coefficients, advection and dilution terms. We present specific examples by analyzing a third order activator-inhibitor mechanism for the kinetic part. We carry out illustrative numerical simulations on two types of growing cones.

IMA Journal of Applied Mathematics, 1996

In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type f... more In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation u, = [D(u)

Discrete and Continuous Dynamical Systems - Series B, 2009

The gregarious behavior of individuals of populations is an important factor in avoiding predator... more The gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form ut = [D(u)ux]x + g(u). The model involves a density-dependent non-linear diffusion coefficient D whose sign changes as the population density u increases. For negative values of D aggregation occurs, while dispersion occurs for positive values of D. We deal with a family of degenerate negative diffusion equations with logistic-like growth rate g. We study the one-dimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the ill-posedness of the partial differential equation problem is included.