
1190SIntroClass
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...

6067SLotkaVolterra
07 Aug 2021   Contributor(s):: Iordanka Panayotova, Maila Hallare
This modeling scenario guides students through the process of fitting the LotkaVolterra 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...

2016Devaki, K. B. and S. Swathi The System of Differential Equations in Prey Predator Model.
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/wpcontent/uploads/2016/03/162.pdf...

2004Hsu, SzeBi  Mathematical Modelling In Biological Science. Class notes
02 Apr 2020   Contributor(s):: Brian Winkel
Hsu, SzeBi. 2014. Mathematical Modelling In Biological Science. Department of Mathematics,TsingHua University TAIWAN. Class Notes. 67 pages.Table of ContentsIntroduction 1 Continuous population model for single species 11.1 Logistic equation...

2013Pescitelli, Monica  Lotka Volterra PredatorPrey Model with a Predating Scavenger. Capstone project
29 Mar 2020   Contributor(s):: Brian Winkel
2013PescitelliLotkaVolterraPredatorPreyWithPredatingScavengerPescitelli, Monica. 2013. Lotka Volterra PredatorPrey Model with a Predating ScavengerAbstract: The classic Lotka Volterra equations are used to model the population dynamicsbetween two species: a predator and...

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

2006Lingefjard, Thomas  Faces of mathematical modeling
25 Mar 2020   Contributor(s):: Brian Winkel
Lingefjard, Thomas. 2006. Faces of mathematical modeling. ZDM. 38(2): 96112.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...

2014Chivers, WJ , Gladstone, W , Herbert, RD , and Fuller, MM  Predatorprey systems depend on a prey refuge.
22 Mar 2020   Contributor(s):: Brian Winkel
Chivers WJ , Gladstone W , Herbert RD , and Fuller MM. 2014. Predatorprey systems depend on a prey refuge. J Theor Biol. 7(360): 271278.See https://pubmed.ncbi.nlm.nih.gov/25058806/ .Abstract:Models of nearexclusive predatorprey systems such as that of the Canadian...

2006Cooke, Kenneth L, Richard H Elderkin, and Wenzhang Huang  PredatorPrey interactions with delays due to juvenile maturation
13 Mar 2020   Contributor(s):: Brian Winkel
2006CookeEtAlPredPreyWithDelaysDueToJuvinileMaturationCooke, Kenneth L, Richard H Elderkin, and Wenzhang Huang. 2006. PredatorPrey interactions with delays due to juvenile maturation. SIAM J. APPL. MATH. 66(3): 10501079.See https://epubs.siam.org/doi/abs/10.1137/05063135...

2005Hirst, H. P.  Using the Historical Development of PredatorPrey Models to Teach Mathematical Modeling
12 Mar 2020   Contributor(s):: Brian Winkel
Hirst, H. P. 2005. Using the Historical Development of PredatorPrey 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.

5015SRunnerSynchronize
13 Jan 2020   Contributor(s):: Eli E Goldwyn
The goal is for students to practice finding and classifying equilibria of a onevariable system in this modeling context while also introducing variables defined on a restricted domain (the circle).

3087SThanosPopulationDynamicsInteractingSpecies
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...

2017Suebcharoen, T.  Analysis of a PredatorPrey Model with Switching and StageStructure for Predator.
07 Mar 2018   Contributor(s):: T. Suebchareon
Suebcharoen, T. 2017. Analysis of a PredatorPrey Model with Switching and StageStructure for Predator. International Journal of Differential Equations. Volume 2017, Article ID 2653124, 11...

2009Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur  Bioeconomic harvesting of a prepredator fishery.
03 Mar 2018   Contributor(s):: Tapasi Das
Das, Tapasi, R. N. Mukherjee, and K. S. Chaurhur. 2009. Bioeconomic harvesting of a prepredator fishery. Journal of Biological Dynamics. 3(5): 447462.See https://pubmed.ncbi.nlm.nih.gov/22880894/ . Abstract: This paper deals with the problem of nonselective harvesting of a...

2011Cao, J., L. Wang, J. Xu  Robust estimation for ordinary differential equation models.
23 Sep 2017   Contributor(s):: Brian Winkel
Cao, J., L. Wang, J. Xu. 2011. Robust estimation for ordinary differential equation models. Biometrics. 67(4): 130513.See https://pubmed.ncbi.nlm.nih.gov/21401565/ .Abstract: Applied scientists often like to use ordinary differential equations (ODEs) to model complex dynamic...

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

2017MBW PredatorPrey Models With Delay And Prey Harvesting
10 Sep 2017   Contributor(s):: Brian Winkel
MBW PredatorPrey Models With Delay And Prey Harvesting. https://mathbio.colorado.edu/index.php/MBW:Predatorprey_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...

2017Unknown  Ten DE Application Problems
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....

2011Pulley, Lucas C.  Analyzing PredatorPrey Models Using Systems of Ordinary Linear Differential Equations.
09 Sep 2017   Contributor(s):: Brian Winkel
Pulley, Lucas C. 2011. Analyzing PredatorPrey 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...

2014Vance, James and Christina Eads  Sensitivity Analysis of a ThreeSpecies Nonlinear Response Omnivory Model with Predator Stage Structure.
08 Sep 2017   Contributor(s):: Brian Winkel
Vance, James and Christina Eads. 2014. Sensitivity Analysis of a ThreeSpecies Nonlinear Response Omnivory Model with Predator Stage Structure. Letters in Biomathematics. 1(1): 7786.See  https://lettersinbiomath.journals.publicknowledgeproject.org/index.php/lib/article/view/153...