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Article or Presentation
170
views
63
downloads
0
comments
1988-Michael_Intriligator-Dagobert_Brito-A_Predator-Prey_Model_of_Guerrilla_Warfare
The purpose of this paper is to analyze guerrilla warfare by means of a dynamic model. The model suggests specific paths for the evolution of such ward and how such wars might be fought or combatted.
simulation
guerilla warfare
warfare
combat
Potential Scenario
200
views
103
downloads
0
comments
2018-LA_Peletier-Ordinary Differential Equations in Pharmacodynamics
Good mix of theory, application, solution technique in a number of areas of applications of differential equations. Develops qualitative behavior issues. Exercises, but not about models, more about the mathematics only.
compartment model
pharmacokinetics
pharmacodynamics
orbits
turnover
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
Potential Scenario
171
views
54
downloads
0
comments
1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
combat model
guerrilla warfare
government
Modeling Scenario
308
views
290
downloads
0
comments
1-190-IntroClass-ModelingScenario
Students go through development of ideas in mathematical modeling with differential equations. They encounter fundamental ideas of unlimited population growth, limited population growth and a predator prey system.
population dynamics
predator-prey
logistic
exponential
graphical interpretations
qualitative analysis
Modeling Scenario
252
views
513
downloads
0
comments
1-091-InvestigatingSlopeFields-ModelingScenario
Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves.
slope fields
population
Modeling Scenario
301
views
135
downloads
0
comments
1-118-SolowEconomicGrowth-ModelingScenario
Students construct and analyze the celebrated Solow-Swan model of economic growth theory. The project is divided into three sequential parts to teach students to understand, develop, and analyze a simple nonlinear model of economic dynamics.
optimization
economics
steady state
growth
Solow-Swan model
capital
production
labor
Golden Rule of Economic Growth
Free Online Textbook
143
views
67
downloads
0
comments
2015-H_Sayama-Intro to Modeling and Analysis of Complex Systems
Introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science.
textbook
text
Potential Scenario
130
views
56
downloads
0
comments
2001-Tsoularis-Analysis of logistic growth models
variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. We further review and compare several such models.
logistic
Gompertz
Verhulst
Pearl and Reed
Bertalanffy
Free Online Textbook
163
views
58
downloads
0
comments
2014-Andre_De Ross-Modeling Population Dynamics
This course is intended as an introduction to the formulation, analysis and application of mathematical models that describe the dynamics of biological populations.
predator-prey
competition
population
growth
bifrucation
text
Potential Scenario
205
views
57
downloads
0
comments
1986-Istvan_Gyori-Connections between compartment systems pipes and integro-differential equations
In this paper we give the mathematical description of models in which the mass transport between compartments requires a given definite time or transit times are distributed according to given probability distribution functions.
physiology
pipeline
compartment
blood
circulation
integro-differential equation
Modeling Scenario
584
views
330
downloads
0
comments
6-020-AlgaePopulationSelf-Replenishment-ModelingScenario
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. A
algae
population
Mexico
qualitative
compartment
linearization
Jacobian
lak
nondimensionalization
pplane
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
415
views
517
downloads
0
comments
6-068-VisualizingPredator-PreyCycles
In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be offering three predator-prey models, each more complex...
nullclines
predator-prey
Geometry
predator
Runge-Kutta
prey
limit cycle
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
314
views
475
downloads
0
comments
1-065-AlgalBlooms-ModelingScenario
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994.
direction fields
tool:dfield
algae
harmful algae blooms
population
compartment
Lake Chapala
Modeling Scenario
311
views
139
downloads
0
comments
1-104-InfectionRisk-ModelingScenario
This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions.
infection
logistic
exponential
covid
carrying capacity
Modeling Scenario
256
views
326
downloads
0
comments
3-072-EarthQuakePartI-ModelingScenario
This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system.
earthquake
vibration
amplitude
resonance
undamped
spring-mass system
General Resource
1053
views
142
downloads
0
comments
Instructor Solutions Second Edition SIMIODE Textbook HTML Version
This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
textbook
html
SIMIODE textbook
Second Edition
Potential Scenario
136
views
71
downloads
0
comments
2002-Fay-The Pendulum Equation
We investigate the pendulum equation q’’(t) + l2 sin(q) = 0 and two approximations for it.
pendulum
Fourier series
Taylor series
numerical solution
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