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  1. 1-190-S-IntroClass

    out of 5 stars 

    05 Mar 2022 | | Contributor(s):: Bill Skerbitz

    Students are led step by step through the development of introductory ideas in mathematical modeling with differential equations. They will encounter the fundamental ideas underlying unlimited population growth (exponential models), limited population growth (logistic models), and a coupled...

  2. 6-067-S-LotkaVolterra

    out of 5 stars 

    07 Aug 2021 | | Contributor(s):: Iordanka Panayotova, Maila Hallare

    This modeling scenario guides students through the process of fitting the Lotka-Volterra model of two differential equations to a real time series observational data. Students use the capabilities of R and R studio, an integrated development environment for R, and the gauseR package, a collection...

  3. 2016-Devaki, K. B. and  S. Swathi -The System of Differential Equations in Prey Predator Model.

    out of 5 stars 

    06 Apr 2020 | | Contributor(s):: Brian Winkel

    Devaki, K. B. and  S. Swathi. 2016. The System of Differential Equations in Prey Predator Model.  International Journal of Multidisciplinary Research and Modern Education. ISSN (Online): 2454 - 6119See http://rdmodernresearch.org/wp-content/uploads/2016/03/162.pdf...

  4. 2004-Hsu, Sze-Bi - Mathematical Modelling In Biological Science. Class notes

    out of 5 stars 

    02 Apr 2020 | | Contributor(s):: Brian Winkel

    Hsu, Sze-Bi. 2014. Mathematical Modelling In Biological Science. Department of Mathematics,Tsing-Hua University TAIWAN. Class Notes. 67 pages.Table of ContentsIntroduction 1 Continuous population model for single species 11.1 Logistic equation...

  5. 2013-Pescitelli, Monica - Lotka Volterra Predator-Prey Model with a Predating Scavenger. Capstone project

    out of 5 stars 

    29 Mar 2020 | | Contributor(s):: Brian Winkel

    2013-Pescitelli-LotkaVolterraPredator-Prey-WithPredatingScavengerPescitelli, Monica. 2013. Lotka Volterra Predator-Prey Model with a Predating ScavengerAbstract: The classic Lotka Volterra equations are used to model the population dynamicsbetween two species: a predator and...

  6. 2017-Páez Chávez, Joseph; Dirk Jungmann; and Stefan Siegmund - Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations

    out of 5 stars 

    27 Mar 2020 | | Contributor(s):: Brian Winkel

    Joseph Páez Chávez,1,2 Dirk Jungmann,3 and Stefan Siegmund. 2017. Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations. International Journal of Differential Equations. Volume 2017, Article ID 1820607, 18 pages.See...

  7. 2006-Lingefjard, Thomas - Faces of mathematical modeling

    out of 5 stars 

    25 Mar 2020 | | Contributor(s):: Brian Winkel

    Lingefjard, Thomas. 2006. Faces of mathematical modeling. ZDM. 38(2): 96-112.See https://subs.emis.de/journals/ZDM/zdm062a3.pdf .Abstract: In this paper I will discuss and exemplify my perspectives on how to teach mathematical modeling, as well as discuss quite different faces of...

  8. 2014-Chivers, WJ , Gladstone, W , Herbert, RD , and Fuller, MM - Predator-prey systems depend on a prey refuge.

    out of 5 stars 

    22 Mar 2020 | | Contributor(s):: Brian Winkel

    Chivers WJ , Gladstone W , Herbert RD , and Fuller MM. 2014. Predator-prey systems depend on a prey refuge. J Theor Biol. 7(360): 271-278.See https://pubmed.ncbi.nlm.nih.gov/25058806/ .Abstract:Models of near-exclusive predator-prey systems such as that of the Canadian...

  9. 2006-Cooke, Kenneth L, Richard H Elderkin, and Wenzhang Huang - Predator-Prey interactions with delays due to juvenile maturation

    out of 5 stars 

    13 Mar 2020 | | Contributor(s):: Brian Winkel

    2006-CookeEtAlPred-PreyWithDelaysDueToJuvinileMaturationCooke, Kenneth L, Richard H Elderkin, and Wenzhang Huang. 2006. Predator-Prey interactions with delays due to juvenile maturation. SIAM J. APPL. MATH.  66(3): 1050-1079.See https://epubs.siam.org/doi/abs/10.1137/05063135...

  10. 2005-Hirst, H. P. - Using the Historical Development of Predator-Prey Models to Teach Mathematical Modeling

    out of 5 stars 

    12 Mar 2020 | | Contributor(s):: Brian Winkel

    Hirst, H. P. 2005. Using the Historical Development of Predator-Prey Models to Teach Mathematical Modeling. In From Calculus to Computers: Using the last 200 years of mathematics history in the classroom. Washington DC: Mathematical Association of America. 7 pp. 

  11. 5-015-S-RunnerSynchronize

    out of 5 stars 

    13 Jan 2020 | | Contributor(s):: Eli E Goldwyn

    The goal is for students to practice finding and classifying equilibria of a one-variable system in this modeling context while also introducing variables defined on a restricted domain (the circle).

  12. 3-087-S-ThanosPopulationDynamicsInteractingSpecies

    out of 5 stars 

    06 Dec 2019 | | Contributor(s):: Blain Patterson, Sarah Elizabeth Ritchey Patterson

    In the end of the “Avengers Infinity War,” the villain Thanos snaps his fingers and turns half of all living creatures to dust with the hope of restoring balance to the natural world. How does this affect the long term behavior of various species? Investigate the validity of his...

  13. 2017-Suebcharoen, T. - Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator.

    out of 5 stars 

    07 Mar 2018 | | Contributor(s):: T. Suebchareon

    Suebcharoen, T. 2017. Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator. International Journal of Differential Equations. Volume 2017, Article ID 2653124, 11...

  14. 2009-Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur - Bioeconomic harvesting of a pre-predator fishery.

    out of 5 stars 

    03 Mar 2018 | | Contributor(s):: Tapasi Das

    Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur. 2009. Bioeconomic harvesting of a pre-predator fishery. Journal of Biological Dynamics. 3(5): 447-462.See https://pubmed.ncbi.nlm.nih.gov/22880894/ . Abstract: This paper deals with the problem of non-selective harvesting of a...

  15. 2011-Cao, J., L. Wang, J. Xu - Robust estimation for ordinary differential equation models.

    out of 5 stars 

    23 Sep 2017 | | Contributor(s):: Brian Winkel

    Cao, J., L. Wang, J. Xu. 2011. Robust estimation for ordinary differential equation models. Biometrics.  67(4): 1305-13.See https://pubmed.ncbi.nlm.nih.gov/21401565/ .Abstract: Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic...

  16. 2017-Zivaripiran, Hossein - Parameter Estimation of Mathematical Models Described by Differential Equations.

    out of 5 stars 

    10 Sep 2017 | | Contributor(s):: Brian Winkel

    Zivaripiran, Hossein. Parameter Estimation of Mathematical Models Described by Differential Equations. PowerPoint. 32 Slides. See - http://www.cs.toronto.edu/~hzp/index_files/presentations/ST2hossein.pdf . Accessed 10 September 2017. Statistical attempts at parameter estimation given...

  17. 2017-MBW- Predator-Prey Models With Delay And Prey Harvesting

    out of 5 stars 

    10 Sep 2017 | | Contributor(s):: Brian Winkel

    MBW- Predator-Prey Models With Delay And Prey Harvesting. https://mathbio.colorado.edu/index.php/MBW:Predator-prey_models_with_delay_and_prey_harvesting . Accessed 10 September 2017.This is a very nice exposition, no problems or data offered, of a biological system and is part of a larger...

  18. 2017-Unknown - Ten DE Application Problems

    out of 5 stars 

    10 Sep 2017 | | Contributor(s):: Brian Winkel

    Ten Application Problems of Differential EquationA list of 10 applications anonymous list with these instructions, “For each problem, set up a differential equation modeling the situation. Be sure to define your variables, state the units being used, and determine the initial condition....

  19. 2011-Pulley, Lucas C. - Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations.

    out of 5 stars 

    09 Sep 2017 | | Contributor(s):: Brian Winkel

    Pulley, Lucas C. 2011. Analyzing Predator-Prey Models Using Systems of Ordinary Linear Differential Equations.  Southern Illinois Universitiy, Honors Theses. Paper 344.See https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=1349&context=uhp_theses .Abstract: The main...

  20. 2014-Vance, James and  Christina Eads - Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure.

    out of 5 stars 

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Vance, James and  Christina Eads. 2014. Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure. Letters in Biomathematics. 1(1): 77-86.See - https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/153...