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Date
Relevance
Technique Narrative
543
views
312
downloads
0
comments
1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.
carbon dioxide
Surface Atmosphere Exchange
bifurcation
fold bifurcation
saddle node
Modeling Scenario
251
views
219
downloads
0
comments
1-135-FishHarvesting-ModelingScenario
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 case the rate of harvesting fish.
population dynamics
fish
stability
bifurcation
harvest
Technique Narrative
382
views
211
downloads
0
comments
1-009-Bifurcation-TechniqueNarrative
We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
bifurcation
qualitative behavior
bifurcation diagram
Modeling Scenario
398
views
608
downloads
0
comments
1-076-ClimateBifurcation-ModelingScenario
We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
energy balance
climate
energy
albedo
Hysteresis
bifurcation
ice-age
greenhouse
balance
Stefan Boltzmann Law
Modeling Scenario
214
views
208
downloads
0
comments
1-134-LanguageDynamics-ModelingScenario
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.
language
compartment
phase lines
bifurcation
switching
Modeling Scenario
275
views
135
downloads
0
comments
1-143-PopulationModelVariationsMATLAB-ModelingScenario
Students will walk through a detailed derivation and review of basic population models (exponential and logistic) to create and understand variations of those models.
population dynamics
ecology
logistic growth
bifurcation theory
slope fields
extinction
harvesting
qualitative analysis
stocking
Modeling Scenario
221
views
292
downloads
0
comments
1-137-SheepGraze-ModelingScenario
In this activity, students will apply graphical analysis (such as phase lines) to determine the long-term predictions of a differential equation model for pasture grass using two different formulas for the herbivore consumption rate.
herbivore
plant
phase lines
bifurcation
overexploitation
sheep
graze
Modeling Scenario
217
views
303
downloads
0
comments
5-015-RunnersSynchronize-ModelingScenario
In this modeling scenario we practice finding and classifying equilibria of a one-variable differential equation. We do this in the context of a phase model which is often a simpler way of studying oscillatory phenomena.
predator
Autonomous equations
oscillation
coupled oscillator
synchrony
runner
prey
Kuramato model
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