
1134SLanguageDynamics
08 Aug 2021   Contributor(s):: Jennifer Crodelle
Students will be introduced to a mathematical model for language dynamics. Specifically, the model describes the change in the fraction of a population speaking one language over another. By answering a list of questions, students will explore how changing the status of a language will alter the...

1135SFishHarvesting
08 Aug 2021   Contributor(s):: Jennifer Crodelle
This modeling scenario will introduce students to the concept of a bifurcation through a fish harvesting model. This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this...

1137SSheepGraze
03 Mar 2021   Contributor(s):: Mary Vanderschoot
One of the most wellknown mathematical models in ecology is the LotkaVolterra predatorprey system of differential equations. Initially, this model was used to analyze interactions between two animal populations. But ecologists discovered that it could also be applied to plant (`prey') and...

2013Herald, Christopher M., Satoko Kurita, and Aleksey S. Telyakovskiy  Simple Climate Models to Illustrate How Bifurcations Can Alter Equilibria and Stability.
02 Apr 2020   Contributor(s):: Brian Winkel
Herald, Christopher M., Satoko Kurita, and Aleksey S. Telyakovskiy. 2013. Simple Climate Models to Illustrate How Bifurcations Can Alter Equilibria and Stability. Journal of Contemporary Water Research & Education. 152:...

2016Barbarossa, Maria Vittoria and Christina Kuttler  Mathematical Modeling of Bacteria Communication in Continuous Cultures.
01 Apr 2020   Contributor(s):: Brian Winkel
Barbarossa, Maria Vittoria and Christina Kuttler. 2016. Mathematical Modeling of Bacteria Communication in Continuous Cultures. Appl. Sci. 6(149): 117.See https://www.researchgate.net/publication/303246621_Mathematical_Modeling_of_Bacteria_Communication_in_Continuous_Cultures...

2010Chicone, C.  Mathematical Modeling and Chemical Kinetics. Notes
26 Mar 2020   Contributor(s):: Brian Winkel
2010ChiconeMathModelingANDChemicalKineticsChicone, C. 2010. Mathematical Modeling and Chemical Kinetics. Notes. 14 pp.Motivated by physical science motion laws the author moves into kinetics and life science applications of differential equations.From early section...

2018Banerjee, Malay, Nayana Mukherjee, and Vitaly Volpert  PreyPredator Model with a Nonlocal Bistable Dynamics of Prey.
25 Mar 2020   Contributor(s):: Brian Winkel
Banerjee, Malay, Nayana Mukherjee, and Vitaly Volpert. 2018. PreyPredator Model with a Nonlocal Bistable Dynamics of Prey. Mathematics. 6(41). 13 pp.See https://www.mdpi.com/22277390/6/3/41 .Abstract: Spatiotemporal pattern formation in integrodifferential equation models of...

2013Beckley, Ross; Cametria Weatherspoon; Michael Alexander; Marissa Chandler; Anthony Johnson, and Ghan S Bhatt  Modeling epidemics with differential equations.
20 Mar 2020   Contributor(s):: Brian Winkel
Ross Beckley, Cametria Weatherspoon, Michael Alexander, Marissa Chandler, Anthony Johnson, and Ghan S Bhatt. 2013. Modeling epidemics with differential equations. Class project Tennessee State University and Philander Smith University.Abstract: Abstract. The well known SIR models...

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...

1143SPopulationModelVariationsMATLAB
17 Feb 2019   Contributor(s):: Bill Skerbitz
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models while learning some basic MATLAB functions for working with differential equations. They will also work with other utilities...

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...

2018Unknown  The Logistic Differential Equation  Notes
03 Mar 2018   Contributor(s):: Brian Winkel
The Logistic Differential Equation. Notes. 7 pp.Goals from the notes:• MATH: To analyze the behavior of solutions of an ordinary differential equation geometrically .• MATH: To analyze stability behavior of equilibria of an ordinary differential equation geometricallyand...

2009Unknown  Bifurcation Analysis
12 Sep 2017   Contributor(s):: Brian Winkel
2009. Bifurcation Analysis – One Dimensional ODEs. Notes. 11 pp.This document contains many rich illustrations of various kinds of bifurcation in the context of applications. E.g. harvesting, magnetometer, spruce budworm,Kywords: differential equation, model, bifurcation, analysis,...

2015Sayama, U.  Intro to Modeling and Analysis of Complex Systems
10 Sep 2017   Contributor(s):: Brian Winkel
Sayama, U. 2015. Intro to Modeling and Analysis of Complex Systems. Geneseo NY: Open SUNY Textbooks. 498 pp.Available at https://textbooks.opensuny.org/introductiontothemodelingandanalysisofcomplexsystems/ . Accessed 10 September 2017.From web site, “Introduction to the...

2009Schaffer, W. M. and T. V. Bronnikova  Controlling malaria: competition, seasonality and 'slingshotting' transgenic mosquitoes into natural populations.
09 Sep 2017   Contributor(s):: Brian Winkel
Schaffer, W. M. and T. V. Bronnikova. 2009. Controlling malaria: competition, seasonality and ‘slingshotting’ transgenic mosquitoes into natural populations. Journal of Biological Dynamics. 3(23): 286304.See https://pubmed.ncbi.nlm.nih.gov/22880835/...

2014Brun, PierreThomas, Neil Ribe, and Basile Audoly  An introduction to the mechanics of the lasso.
08 Sep 2017   Contributor(s):: Brian Winkel
Brun, PierreThomas, Neil Ribe, and Basile Audoly. 2014. An introduction to the mechanics of the lasso. Proc. R. Soc. A 470. 18 pp.See https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014.0512 .Abstract: Trick roping evolved from humble origins as a cattle catching tool into...

2012Yuan, Yuan  A coupled plankton system with instantaneous and delayed predation
08 Sep 2017   Contributor(s):: Brian Winkel
Yuan, Yuan. 2012. A coupled plankton system with instantaneous and delayed predation. Journal of Biological Dynamics. 6(2): 148165.See https://www.tandfonline.com/doi/full/10.1080/17513758.2010.544409 .We present two simple plankton population models: one has instantaneous...

2016deBoer, Rob J.  Population Dynamics: A Graphical Approach  Text
06 Sep 2017   Contributor(s):: Brian Winkel
deBoer, Rob J. 2016 .Modeling Population Dynamics: A Graphical Approach. http://tbb.bio.uu.nl/rdb/books/mpd.pdf . Accessed 6 September 2017. 193 pp.From the Preface,“This book is an introduction into modeling population dynamics in ecology. Because there are several good...

2014De Ross, Andre M.  Modeling Population Dynamics  Text
05 Sep 2017   Contributor(s):: Brian Winkel
De Ross, Andre M. 2014. Modeling Population Dynamics. OnLine text. 222 pp.https://staff.fnwi.uva.nl/a.m.deroos/downloads/pdf_readers/syllabus.pdf . Accessed 4 September 2017From the Introduction to the text, “This course is intended as an introduction to the formulation,...

2017Stan, GuyBart  Modelling in Biology.
02 Sep 2017   Contributor(s):: Brian Winkel
2017. Stan, GuyBart. Modelling in Biology. Class Notes. Imperial College of London. 71 pp.Keywords: differential equation, model, stability, equilibrium, bifurcation, mass action, spring mass, limit cycles.This is a very rich set of notes, rich in examples and ideas for modeling. In...