-
1-009-S-Text-Bifurcation
31 May 2015 | | Contributor(s):: Edward Swim
-
1-134-S-LanguageDynamics
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...
-
1-135-S-FishHarvesting
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...
-
1-137-S-SheepGraze
03 Mar 2021 | | Contributor(s):: Mary Vanderschoot
One of the most well-known mathematical models in ecology is the Lotka-Volterra predator-prey 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...
-
1-143-S-PopulationModelVariationsMATLAB
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...
-
2006-Cooke, Kenneth L, Richard H Elderkin, and Wenzhang Huang - Predator-Prey interactions with delays due to juvenile maturation
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...
-
2009-Schaffer, 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(2-3): 286-304.See https://pubmed.ncbi.nlm.nih.gov/22880835/...
-
2009-Unknown - 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,...
-
2010-Chicone, C. - Mathematical Modeling and Chemical Kinetics. Notes
26 Mar 2020 | | Contributor(s):: Brian Winkel
2010-Chicone-MathModelingANDChemicalKineticsChicone, 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...
-
2012-Yuan, 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): 148-165.See https://www.tandfonline.com/doi/full/10.1080/17513758.2010.544409 .We present two simple plankton population models: one has instantaneous...
-
2013-Beckley, 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...
-
2013-Herald, 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:...
-
2014-Brun, Pierre-Thomas, Neil Ribe, and Basile Audoly - An introduction to the mechanics of the lasso.
08 Sep 2017 | | Contributor(s):: Brian Winkel
Brun, Pierre-Thomas, 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...
-
2014-De 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,...
-
2015-Sayama, 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/introduction-to-the-modeling-and-analysis-of-complex-systems/ . Accessed 10 September 2017.From web site, “Introduction to the...
-
2016-Barbarossa, 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): 1-17.See https://www.researchgate.net/publication/303246621_Mathematical_Modeling_of_Bacteria_Communication_in_Continuous_Cultures...
-
2016-deBoer, 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...
-
2017-Stan, Guy-Bart - Modelling in Biology.
02 Sep 2017 | | Contributor(s):: Brian Winkel
2017. Stan, Guy-Bart. 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...
-
2017-Suebcharoen, T. - Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator.
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...
-
2018-Banerjee, Malay, Nayana Mukherjee, and Vitaly Volpert - Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey.
25 Mar 2020 | | Contributor(s):: Brian Winkel
Banerjee, Malay, Nayana Mukherjee, and Vitaly Volpert. 2018. Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey. Mathematics. 6(41). 13 pp.See https://www.mdpi.com/2227-7390/6/3/41 .Abstract: Spatiotemporal pattern formation in integro-differential equation models of...