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    Potential Scenario
    122

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    62

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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
    139

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    79

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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
    Potential Scenario
    170

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    38

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    1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
    A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.
    plantoscillationdelaycircumnutationturning
    Modeling Scenario
    294

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    321

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    1-088-RoomTemperature-ModelingScenario
    Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken).
    environmentclimatetemperatureNewton's Law of Coolingcoolingperiodic function
    Potential Scenario
    145

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    76

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    2010-Keesom-EtAl-Fishing for Answers Investigating Sustainable Harvesting Ra
    The purpose of this report is to determine and propose a model by which an optimal harvesting frequency can be determined to maintain a steady population of Alaskan salmon.
    fisheriesEuler's methodnonlinearlogistic harvestingcanabalismsalmon
    Free Online Textbook
    216

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    55

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    2016-I-Liang_Chern-Mathematical Modeling_and_Ordinary_Differential_Equations
    We let the author's Table of Contents speak for itself.
    differential equationsmodelingtextbook
    Potential Scenario
    122

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    54

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    2001-Knisley-Kerley-Using data to motivate the models used in introductory differential equations
    In this paper, the data itself is used to motivate mathematical models in introductory mathematics courses. In doing so, various regression and optimization techniques are illustrated.
    regressionlogisticTorricelli's Lawgrowthperiodic process
    Potential Scenario
    159

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    71

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    1935 GFGause Article Predator Prey Oscillations
    N/A
    Lotka-Volterrapredatorparameciumpreycycleoscillate
    Potential Scenario
    238

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    57

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    2011-Radouane_Yafia-A Study of Differential Equations Modeling Malignant Tumor Cells in Competition with Immune System
    In this paper, we present a competition model of malignant tumor growth that includes the immune system response. The model considers two populations: immune system (effector cells) and population of tumor (tumor cells).
    Immunologytumorhopf bifrucation
    Modeling Scenario
    250

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    499

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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
    Modeling Scenario
    212

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    226

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    6-075-LorenzSystemSimulation-ModelingScenario
    The Lorenz system is examined by students as a simple model of chaotic behavior or strange attractor. MATLAB code is created to find the numerical solutions of the Lorenz’ system of nonlinear ordinary differential equations using various parameters.
    chaososcillatorLorenzwaterwheelstrange attractorbifurcation effect
    Potential Scenario
    154

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    56

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    2006-Cooke-Elderkin-Huang-Predator-Prey interactions with delays due to juvenile maturation
    This paper focuses on predator-prey models with juvenile/mature class structure for each of the predator and prey populations in turn, further classified by whether juvenile or mature individuals are active with respect to the predation process.
    predator-preyhost-parasitebifurcationage structrematuration delay
    Potential Scenario
    153

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    52

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    2004-Jones-Song-Thomas-Controlling wound healing through debridement
    In this article, a system of differential equations that models slough/wound interaction is developed.
    bacteriawound healinghealingderidingisocline
    Potential Scenario
    197

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    57

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    2003-Yildirim-Mackey-Feedback Regulation in the Lactose Operon
    A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented.
    mRNAlactoselactose operonfeedback regulation
    Potential Scenario
    121

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    39

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    2008-Luis_San_Andrés-Dynamic Response of Second Order Mechanical Systems with Viscous Response Forces
    Walk through the cases in context of second order linear constant coefficient differential equation with driving function
    driving functionviscousmechanical system
    Article or Presentation
    184

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    53

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    2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity
    We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.
    optimizationdiscoveryFourierFourier seris
    Modeling Scenario
    391

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    265

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    5-076-LanchesterLaws-ModelingScenario
    Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
    Lanchester's lawssensitivity analysisanalysis
    Potential Scenario
    177

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    61

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    2011-Nancy_Rodrıguez-Applied Partial Differential Equations in Crime Modeling and Biological Aggregation
    In the first part we study a fully-parabolic system of PDEs for residential burglary ‘hotspots’ (spatio-temporal areas of high density of crime). In this work we are concerned with the existence and uniqueness of solutions of this model. In
    biologyDiffusionKeller-Segel modelchemotaxiscrime
    Article or Presentation
    173

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    52

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    2010-Kar-Chakraborty-Bioeconomic_modelling_of_a_prey_predator_system_using_differential_algebraic_equations
    We propose a biological economic model based on prey-predator dynamics where the prey species are continuously harvested and predation is considered with type II functional response.
    economicsbifurcationharvestfisheryequilibriumdifferential algebraic equation
    Potential Scenario
    248

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    2009-Das-EtAl-Bioeconomic harvesting of a pre-predator fishery
    This paper deals with the problem of non-selective harvesting of a prey–predator system by using a reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis.
    predator-preyharvestingPontryagin’s maximum principlebioeconomicbionomic equilibriumbiotechnical productivitycatch-rate functionoptimal equilibrium