Jose Flores

Emeritus 2023-Infinity.
Professor of Mathematics at USD 1989-2023.
PhD. in Numerical Analysis from the University of Iowa.
Dissertation: "Iterative Methods for Solving Integral Equations of Second Kind" directed by Dr. Kendall E. Atkinson.

Applied Mathematics, Mathematical Modeling, Numerical Linear Algebra, Numerical Solutions for Ordinary and Partial Differential Equations, Numerical Analysis, and Scientific Computing.

My research interest is in the areas of Mathematical Ecology, Mathematical Modeling applied to Population Dynamics, Scientific Computing, Ecological Networks, and Mathematical Modeling in Biodiversity in polluted environments.

International Collaborator in the grant "The interplay between phenological, adaptive and long-term dynamics of ecological networks " , Fondecyt-Chile, (2015 - 2019)
Visiting reserach faculty: International Collaborator in the grant "The interplay between phenological, adaptive and long-term dynamics of ecological networks " , Fondecyt-Chile, (2015 - 2015)
External colaborator in the grant "Multistability and periodicity on predator-prey models due to ecological phenomena affecting some populations", Pontificia Universidad Catolica de Valparaiso and Fondecyt, (2012 - 2014)
Visiting research faculty in the grant "Multistability and periodicity on predator-prey models due to ecological phenomena affecting some populations", Pontificia Universidad Catolica de Valparaiso and Fondecyt, (2012 - 2014)
Governor's Faculty Technology Grant, State of South Dakota, (2003 - 2003)
Governor's Faculty Technology Grant "Teaching Tools for Multivariable Calculus" , State of South Dakota, (2002 - 2002)
Governor's Faculty Awards for Teaching with Technology, State of South Dakota, (2001 - 2001)
USD Office of Research Proposal Incentive Award, USD, (2001 - 2001)
A Web-based Mathematical Tutorial , USD, (2000 - 2000)
Enhancing Calculus Teaching with Technology, State of South Dakota Eisenhower Grant, (2000 - 2000)
USD Office of Research Proposal Incentive Award, USD, (1998 - 1998)
Governor's Faculty Technology Grant "Implementation of Multivariable Calculus Using Technology, State of South Dakota, (1998 - 1998)
Computer Classroom For the Upper Division Courses in Mathematical Sciences, NSF, (1997 - 1999)
Creating New Undergraduate Research Mentors at the University of South Dakota, USD Bush Mini-Grant Program, (1996 - 1996)

Citations listed below are presented in a standardized, modified format for display purposes only. They do not necessarily reflect the preferred style and conventions of the faculty member or discipline.

Arancibia-Ibarra, Claudio, Flores, Jose, and van Heijster, Peter. Stability analysis of a modified Leslie-Gower predation model with weak Allee effect on the prey . Frontiers in Applied Mathematics and Statistics: Dynamical Systems, 2022.
Arancibia-Ibarra, Claudio, and Flores, Jose. Dynamics of a Leslie-Gower predator-prey model with Holling type II functional response, Allee effec and a generalist predator. Mathematics and Computers in Simulation (MATCOM). Elsevier, 2021.
Arancibia-Ibarra, Claudio, Bode, Michael, Flores, Jose, and van Heijter, Peter . Turing Patterns in a diffusive Holling-Tanner predator-prey model with an alternative food source for the predator. Elsevier: Comunications in Nonlinear Science and Numerical Simulation, 2021.
Wesner, Jeff, Van Peursem, Dan, Flores, Jose, Lio, Yuhlong, and Wesner, Chelsea. Forecasting hospitalizations due to COVID-19 in South Dakota, USA, 218-229. Vol. 5, Iss. 2 Journal of Healthcare Informatics Research, 2021.
Arancibia-Ibarra, Claudio , Aguirre, Pablo, Flores, Jose, and van Heijter, Peter. Bifurcation Analysis of a predator-prey model with intra-specific interactions and ratio-dependent functional response. Science Direct: Applied Mathematics and Computation, 2021.
Arancibia-Ibarra, Claudio, and Flores, Jose. Modelling and analysis of a modified May-Holling-Tanner predator-prey model with Allee effect on the prey and an alternative food source for the predator. Mathematical Bioscience and Engineering, 2020.
Arancibia-Ibarra, Claudio, Flores, Jose, Bode, Michael, Pettet, Graeme, and van Heijster, Peter. A Modified May-Holling-Tanner predator-prey model with multiple Allee effect on the prey and an alternative food source for the predator. Discrete and Continuous Dynamical Systems Series B. AIMS' Journals, 2020.
Arancibia-Ibarra, Claudio, Flores, Jose, Pettet, Graeme, and van Heijster, Peter. A Holling-Tanner predator-prey model with strong Allee effect . Vol. 29, Iss. 11 Singapore: International Journal of Bifurcation and Chaos, 2019.
Flores, Jose. Research in Mathematical Ecology and the Struggle for Existence. In The third score The Harrinton Lectures 1993-2013. Vermilluion, South Dakota : College of Arts & Sciences USD , 2019.
Flores, Jose, and González-Olivares, Eduardo . A modified Leslie-Gower predator-prey model with ratio-dependent functional response and alternative food for the predator., 2313-2328. Vol. 40 Mathematical Methods in Applied Sciences, 2017.
Chowell, Gerardo , Simonsen, Lone, Fuentes, Rodrigo, Flores, Jose, Miller, Mark A., and Viboud, Cécile . Severe mortality impact of the 1957 influenza pandemic in Chile.., Editors Jonathan Van-Tam. Journal of Influenza and Other Respiratory Viruses, 2016.
Viboud, Cécile , Simonsen, Lone, Fuentes, Rodrigo, Flores, Jose, Miller, Mark A., and Chowell, Gerardo . Global mortality impact of the 1957-1959 influenza pandemic, 738-745. Vol. 213 The Journal Infectious Diseases, 2016.
González-Olivares, Eduardo , and Flores, Jose. Consequences of multiple Allee effect in an open access fishery model, S101-S121. Vol. 23, Iss. special Journal of Biological Systems, 2015.
Chowell, Gerardo , Simonsen, Lone, Flores, Jose, Miller, Mark A., and Viboud, Cécile. Spatial-temporal mortality patterns of the 1918 influenza pandemic in Chile: delayed impact to the second year of circulation and latitudinal variation in disease burden. Vol. 20, Iss. 11 Emerging Infectious Diseases, 2014.
Flores, Jose, and González-Olivares, Eduardo . Dynamics of a predator-prey model with Allee effect on prey and ratio-dependent functional response, 59-66. Vol. 18 Ecological Complexity, 2014.
Garay-Narvaez, Leslie , Flores, Jose, Arim, Matias , and Ramos-Jiliberto, Rodrigo. Food web modularity and biodiversity promote species persistence in polluted environments, 583-249. Vol. 123, Iss. 5 OIKOS, 2014.
Aguirre, Pablo, Flores, Jose, and Gonzalez-Olivares, Eduardo . Bifurcations and global dynamics in a predator-prey model with strong Allee effect on prey and ratio-dependent functional response, 235-249. Vol. 16 Journal of Nonlinear Analysis Series B: Real World Applications, 2014.
Garay-Narvaez, Leslie , Arim, Matias , Flores, Jose, and Ramos-Jiliberto, Rodrigo. The more polluted the environment, the more important biodiversity is for food web stability, 583-249. Vol. 123, Iss. 5 OIKOS, 2013.
González-Olivares, Eduardo, and Flores, Jose. A predator-prey model with weak Allee effect on prey and ratio-dependent functional response. In 13th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE 2013, editors I. Hamilton & J. Vigo-Aguiar eds., 757-768. Vol. 2 Almeria-Spain: Proceedings of the 2013: 13th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE 2013, 2013.
González-Olivares, Eduardo , González-Yañez, Betsabe, Mena-Lorca, Jaime, and Flores, Jose. Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey. Vol. 10, Iss. 2 Mathematical Biosciences and Engineering , 2013.
Leung, M-R, Marchand, M., Stykel, S. , Huynh, M, and Flores, Jose. The Effect of Localized Oil Spills on the Atlantic Loggerhead Turtle Population Dynamics. Vol. 2, Iss. 3 Open Journal of Ecology, 2012.
Valdovinos, Fernanda, Moisset de Espané, Pablo, Flores, Jose, and Ramos-Jiliberto, Rodrigo. Adaptive foraging allows the maintenance of biodiversity of pollination networks in spite of nestedness. OIKOS, 2012.
Ramos-Jiliberto, Rodrigo , Valdovinos, Fernanda , Moisset de Espanés , Pablo, and Flores, Jose. Topological plasticity increases robustness of mutualistic networks, 896-904. Vol. 81 Journal of Animal Ecology, 2012.
Flores, Jose, and González-Olivares, Eduardo. A predator-prey model with ratio-dependent functional response and strong Allee effect on prey. Proceedings of the 9th WSEAS International conference on Mathematical Biology and Ecology, 2012.
Gonzalez-Olivares, Eduardo, Rojas-Palma, Alejandro, Mena-Lorca, Jaime , and Flores, Jose. Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey, 336-381. Vol. 35, Iss. 1 Applied Mathematical Modelling, 2011.
Flores, Jose, and Gonzalez-Olivares, Eduardo. Consequences of double Allee effect on the number of limit cycles in a predator-prey model, 3449-3463. Vol. 62 Computer and Mathematics with Applications, 2011.
Valdovinos, Fernanda, Ramos-Jiliberto, Rodrigo, Flores, Jose, Espinoza, Claudia, and Lopez, Gioconda. Structure and Dynamics of Pollination Networks: The Role of Alien Plants, 1190-1200. Vol. 118, Iss. 8 OIKOS: Synthesising Ecology, 2009.
Ramos-Jiliberto, Rodrigo, Mena-Lorca, Jaime , Flores, Jose, and Morales, Waldo. Role of Inducible Defenses in the Stability of a Tritrophic System, 183-192. Vol. 5 Journal of Ecological Complexity, 2008.
Ramos, Carolina, Simonetti, J.A. , Flores, Jose, and Ramos-Jiliberto, Rodrigo. Modeling the management of fragmented forests. Is it possible to recover the original tree composition? The case of the Maulino forest in Central Chile, 2236-2243. Vol. 255, Iss. 7 Journal of Forest Ecology and management, 2008.
Gonzalez-Olivares, Eduardo, Meneses-Alcay, Hector, Mena-Lorca, Jaime, Flores, Jose, and Gonzalez-Yanez, Betsabe. Allee effect, emigration and immigration in a class of predator-prey models, 195-215. Vol. 3, Iss. 1-2 Biophysical Reviews and Letters , 2008.
Flores, Jose, Gonzalez-Olivares, Eduardo, Gonzalez-Yanez, Betsabe, and Mena-Lorca, Jaime . Consequences of Depensation in a Bio-Economic Model for Open-Access Fishery. BIOMAT 2006 Proceedings: International Symposium on Mathematical and Computational Biology , 2006.
Flores, Jose. Numerical Solution of a First Kind Integral Equation of Potential Theory, 471-486. Vol. 9, Iss. 5 Inverse Problems in Engineering, 2002.
Saavedra-Guzman, Jorge, and Flores, Jose. Numerical Solution of Laplace's Equation on Non-Simply Connected Regions in R^2. Vol. 78, Iss. 2 International Journal of Computer Mathematics, 2001.
Flores, Jose, and Saavedra-Guzman, Jorge. Iterative Methods Numerical Solution of Laplace's Equation on Non-Simply Connected Regions in R^2. Proceedings do XXIII CNMAC. Uma Publicacao da Sociedade Brasileira de Matematica Aplicada e Computacional, 2000.
Flores, Jose. The Conjugate Gradient Method in the Presence of Clustered Eigenvalues. Vol. 19, Iss. 2 SIGSMALL/PC Notes, ACM Press, 1993.
Atkinson, Kendall E., and Flores, Jose. The Discrete Collocation Method for Nonlinear Integral Equations, 195-213. Vol. 13 IMA Journal of Numerical Analysis, 1993.
Flores, Jose. The conjugate Gradient Method for Solving Fredholm Integral Equations of Second Kind, 78-94. Vol. 48 International Journal of Computer Mathematics, 1992.

Flores, Jose, and Arancibia-Ibarra, Claudio, Dynamics of a Leslie-Gower predator-prey model with Holling type II functional response, a generalist predator and Allee effect on the prey.. Presented at the Models in Population Dynamics, Ecology and Evolution (MPDEE 2022), Torino, Italy. (June 13, 2022)
Flores, Jose, Matrix Population Models: Structured Populations. Presented at the Primer Encuentro Suroccidental de Matematicas y Matematicas Aplicadas, Cali, Colombia. (November 19, 2019)
Flores, Jose, Pattern Formation in Ratio-Dependent Predator-Prey models with Dispersion. Presented at the Center for Genomic, Ecology and Environment (GEMA), Santiago, Chile. (August 01, 2018)
Flores, Jose, Dispersion in the dynamics of predator-prey models with ratio-dependent functional response. Presented at the Fifth International and Interdisciplinary Workshop on Mathematical Modeling of Environment and Evolution on Social and Life Process (5th IIWEE), Villa de Leyva, Colombia.. (June 28, 2018)
Flores, Jose, Dynamics of predator-prey models with ratio-dependent functional response. Presented at the X Congreso LatinoAmericano de Biomatematica, Cuzco, Peru. (August 07, 2017)
Flores, Jose, Matrix Population Models . Presented at the Mathematical and Theoretical Biology Institute, Tempe, Arizona. (June 13, 2017)
Flores, Jose, Analysis of Reaction Diffusion Equations Based Models . Presented at the Mathematical and Theoretical Biology Institute, Tempe, Arizona. (June 22, 2016)
Flores, Jose, Interacting Population Models . Presented at the Mathematical and Theoretical Biology Institute, Tempe, Arizona. (June 15, 2016)
Flores, Jose, Matrix Population Models . Presented at the Mathematical and Theoretical Biology Institute, Tempe, Arizona. (June 10, 2016)
Flores, Jose, Discrete Population Dynamics. Presented at the Mathematical and Theoretical Biology Institute, Tempe, Arizona. (June 09, 2016)
Flores, Jose, A Finite-Differences Algorithm for a Pest Control Model. Presented at the X INTERNATIONAL SEMINAR ON BIOMATHEMATICS, Tingo Maria, Peru. (August 2014)
Flores, Jose, Dynamics of Predator-prey interaction under Allee effects.. Presented at the Strengthening the Nation Through Diversity, Innovation and Leadership in STEM, San Antonio, Texas. (October 2013)
Flores, Jose, Endometriosis Mathematical Model: Cells chemotaxis movements. Presented at the IX INTERNATIONAL SEMINAR ON BIOMATHEMATICS, Cusco, Peru. (August 07, 2013)
Flores, Jose, A modified Holling-Tanner predator-prey model with ratio-dependent functional response. Presented at the Annual conference of the Society for Mathematical Biology, Tempe, AZ. (June 2013)
Flores, Jose, A Tale of Two Models. Presented at the Mathematics on the Northern Plains, Sioux Falls. (April 2013)
Flores, Jose, Consequences of a Double Allee effect in predator-prey model with ratio-dependent functional response. Presented at the International Symposium on Mathematical and Computational Biology (BIOMAT-2012), Tempe, Arizona, USA. (November 11, 2012)
Flores, Jose, Bifurcation analysis of a predator-prey model with ratio-dependent functional response. Presented at the VIII SEMBIOMAT, Huaraz, Peru. (August 07, 2012)
Flores, Jose, A Gause predator-prey model with double Allee effect on prey and ratio-dependent functional response. Presented at the BIOCOMP2012 Conference: Mathematical Modeling and Computational Topics in Biosciences, Vietri Sul Mare, Italy.. (June 04, 2012)
Flores, Jose, A Gause predator-prey model with double Allee effect on prey and ratio-dependent functional response. Presented at the Conference in Mathematical Ecology, Lincoln, Nebraska.. (April 14, 2012)
Flores, Jose, Dynamics of a predator-prey model with strong Allee effect on prey hyperbolic ratio-dependent functional response. Presented at the Seminar: Department of Mathematics and Computer Sciences at Angelo State University, San Angelo, TX, San Angelo, Texas.. (February 17, 2012)
Flores, Jose, A predator-prey model with ratio-dependent functional response and strong Allee effect on prey. Presented at the 9th WSEAS International conference on Mathematical Biology and Ecology (MABE'12), Harvard, cambridge, MA.. (January 26, 2012)
Flores, Jose, A predator-prey model with ratio-dependent functional response and strong Allee effect on prey. Presented at the Heterogeneity and Ecologies: delay and partial differential equations, bifurcations and optimal control in epidemiology, Arizona State University, Tempe, AZ.. (June 02, 2011)
Flores, Jose, A ratio-dependent predator-prey model with Allee effect on the prey. Presented at the 10th International Symposium on Mathematical and Computational Biology, Rio de Janeiro, Brazil.. (July 29, 2010)
Flores, Jose, Dynamical complexities in the Leslie-Gower predator-prey model as consequence of the Allee effect on prey. Presented at the Mathematical and Theoretical Biology Institute, ASU, Tempe, AZ.. (July 23, 2010)
Flores, Jose, Using the internet as a tool in teaching mathematics. Presented at the Innovative Strategies for Science Education, Santiago, Chile. (August 29, 2008)
Flores, Jose, Using the internet as a tool to teach mathematics. Presented at the Innovative Strategies for Science Education.”, Universidad de Talca, Santiago, Chile.. (August 29, 2008)
Flores, Jose, Multiple attractors in a Gause type predator-prey model with Allee effect on prey and a non-monotonic functional response. Presented at the VIII Chilean Meeting in Mathematical Ecology, Talca, Chile. (August 28, 2008)
Flores, Jose, Mentoring prospect PhD Students to attend US institutions. Presented at the Fulbright-Chile Mentoring Series, Instituto Chileno-Norteamericano, Santiago, Chile. (August 19, 2008)
Flores, Jose, Computational Mathematics . Presented at the Fulbright Senior Specialist, Instituto de Matematicas, Valparaiso Chile. (August 2008)
Flores, Jose, Maplets for Multivariable Calculus. Presented at the The International Conference on Technology in Collegiate Mathematics, San Antonio, Texas. (March 2008)
Flores, Jose, Multiple Allee Effect in a Bio-economic Model. Presented at the International Symposium on Mathematical and Computational Biology, Amarcaos dos Buzios, Rio de Janeiro. (November 2007)
Flores, Jose, Consequences of Depensation in a Bio-Economic Model for Open-Access Fishery. Presented at the International Symposium on Mathematical and Computational Biology, Federal University of Amazonas, Manaus, Brazil. (November 2006)
Flores, Jose, MapleNet: A tool to teach Mathematics over the Internet. Presented at the MECESUP Workshop, Universidad de Tarapaca, Arica, Chile.. (August 2006)
Flores, Jose, and Mena-Lorca, Jaime, Modelo Espacial de Control de la Mosca de la Fruta Usando Técnica de Esterilización de Insectos en la Primera Región de Chile. Presented at the Congreso Latinoamericano de Biología Matemática, Tandil, Argentina. (November 2005)
Flores, Jose, Computational Models for Tritrophic food Chains. Presented at the Mathematical Ecology Seminar, Instituto de Mathematicas, PUCV, Valparaiso, Chile.. (August 2005)
Flores, Jose, MapleNet: A tool to improve the teaching of Mathematics over the Internet. Presented at the MECESUP Workshop, Universidad de Conepcion, Concepcion , Chile.. (August 2005)

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