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    Modeling Scenario
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    444

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    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...
    nullclinespredator-preyGeometrypredatorRunge-Kuttapreylimit cycle
    Modeling Scenario
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    386

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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.
    phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation
    Potential Scenario
    169

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    56

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    1977-Michael_Mackey-Leon_Glass-Oscillation and Chaos in Physiological Control Systems
    First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillation.
    sensitivitychaosparametersRespirationdelayblood cells
    Potential Scenario
    141

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    69

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    2017-Guy-Bart_Stan-Modelling in Biology
    This is a very rich set of notes, rich in examples and ideas for modeling. In almost all cases after a model is introduced in real context there is attention to stability analysis.
    spring massbifurcationmass actionlimit cycles
    Potential Scenario
    140

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    52

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    1935 GFGause Article Predator Prey Oscillations
    N/A
    Lotka-Volterrapredatorparameciumpreycycleoscillate
    Modeling Scenario
    278

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    507

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    10-100-InsectOutbreaks-ModelingScenario
    We use a system of difference equations that incorporates a temperature-dependent MPB population growth rate to model the outbreak and recovery cycle in mountain pine beetle-infested forests.
    ecologyclimate changeinsectinsect outbreaksinsect outbreaksolitary wave
    Potential Scenario
    219

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    87

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    2017-Chávez-EtAl-Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations
    The paper is concerned with the development and numerical analysis of mathematical models used to describe complex biological systems in the framework of Integrated Pest Management (IPM).
    bifurcationschaosimpulsive modellimit cycleshysteretic effectsperiod-doubling cascades
    Potential Scenario
    151

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    43

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    1972-Suresh_Sethi-Optimal Control of the Vidale-Wolfe Advertising Model
    This paper considers an optimal-control problem for the dynamics of the Vidale-Wolfe advertising model, the optimal control being the rate of advertising expenditure to achieve a terminal market share within specified limits.
    Optimal Control Theoryadvertisingsales
    Technique Narrative
    362

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    186

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    2-001-NumericalMethodsComparisons-TechniqueNarrative
    This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
    Euler's methodimproved Euler's methodRK3 methodsRK4 methodsorder of accuracyabsolute errorCPU time
    Modeling Scenario
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    122

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    1-089-SpreadOfDisease-ModelingScenario
    In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with only a College Algebra background, can still enjoy differential equation...
    SIR modelProportionderivativedifference quotientSleeping Beautycontagious disease
    Potential Scenario
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    56

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    2011-Cruz-Aponte-Herrera-Valdez-Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administrati
    We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters.
    vaccinationinfectionSIRepidemic
    Potential Scenario
    248

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    79

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    2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
    The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
    HangtimeTauberian IdentitiesRoad RunnerWile E. Coyote
    Potential Scenario
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    60

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    spring massoscillationHooke's Lawcoupled springsperiodicforcing functionphase portrait
    Potential Scenario
    112

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    66

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    2006-Shigui_Ruan-Delay differential equations in single species dynamics
    In this survey, we shall review various delay differential equations models arising from studying single species dynamics.
    allee_effectdelayed biological systemsfood limitperiodiciityrecruitment modelRegulation of Haematopoiesis
    Potential Scenario
    125

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    73

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    2003-Fay-Graham-Coupled spring equations
    Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described.
    massoscillationspring\coupled springsperiodicfporcing