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    Potential Scenario
    233

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    67

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    2006-Graves-Peckham-Pastor-2D differential equations model for mutualism
    We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions.
    population dynamicsLotka-Volterragrowth ratemutualismLichen
    Potential Scenario
    146

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    95

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    2018-Banerjee-EtAl-Prey-Predator Model with a Nonlocal Bistable Dynamics of Prey
    The primary goal of our present work is to consider nonlocal consumption of resources in a spatiotemporal prey-predator model with bistable reaction kinetics for prey growth in the absence of predators.
    predator-preynonlocal consumptionTuring bifurcationspatial Hopf bifurcationspatio-temporal patternprey growth
    Potential Scenario
    157

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    72

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    2005-Saifullah-Mathematical Modeling With Differential Equations
    This article aims to provide the students some basic modeling skills, which will have applications to a wide variety of problems.
    species interactionsword equationinteractive software
    Potential Scenario
    203

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    75

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    2016-Devaki-Swathi-System of Differential Equations in Prey Predator Model
    Predation relationship exists in ecological niches throughout the world. This is the species interaction which will be mathematically analyzed and embodied in this work.
    extinctionCoevolutionpredatorLotka Volterra equationspre
    Potential Scenario
    169

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    52

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    2012-Ogunrinde-Sunday-On some models based on second order differential equation
    This paper presents some models based on second order differential equations. Such models include interaction between different kinds of species in an environment and pricing policy for optimum inventory level of a firm.
    species interactionpricing policyoptimal inventory
    Article or Presentation
    183

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    47

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    2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Population_Growth
    We estimate the parameters present in several differential equation models of population growth, specifically single species exponential and logistic growth, and multiple species competition and predation models.
    population modelparameter estimationpopulationparameter
    Potential Scenario
    160

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    52

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    2018-Winkle-Igoshin-Bennett-Josic-Ott-Modeling_Mechanical_Interactions_in_Growing_Populations_of_Rod-Shaped_Bacteria
    Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions.
    bacteriaagent-basedpopulationbrod-shapedcellular growth
    Potential Scenario
    153

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    65

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    2017-Anders_Kallen-Single species models in continuous time
    Part of a series of Lecture notes this lecture contains rich materials on logistic harvest models, spruce budworms, and chemostat.
    chemostatlogisticharvestspruce budworm
    Potential Scenario
    151

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    74

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    2015-Sebesyen-Farago-Invasive Species Model with Linear Rat Harvesting on Easter Island
    In this paper we suggest a natural modification of this model. Namely, we will investigate the case where the amount of the rats is decreased due to some external factor, e.g., exterminations by the people.
    carrying capacityharvestEaster Islandinvasie especiesratsRoughgarden theorem.
    Potential Scenario
    199

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    64

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    0

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    2011-Brian_Winkel-Parameter Estimates in Differential Equation Models for Population Growth
    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models.
    logisticpopulationparameciaGausegradient search
    Potential Scenario
    226

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    75

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    2014-Vance-Eads-Sensitivity Analysis of a Three-Species Nonlinear Response Omnivory Model with Predator Stage Structure
    We investigate a three-species nonlinear response omnivory model incorporating stage structure in the top predator. The model consists of four coupled ordinary differential equations involving fourteen parameters.
    stage structuresensitivity analysismortalityomnivoreomnivory modelsearch rates
    Potential Scenario
    124

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    71

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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
    191

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    61

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    2006-TK_Kar-Controllability and optimal harvesting of a prey–predator model incorporating a prey refuge
    This paper deals with a prey–predator model incorporating a prey refuge and harvesting of the predator species.
    survivalpredator-preyharvestrefugePontryagin’s maximal principlehidingoptimal harvest
    Potential Scenario
    190

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    54

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    1975-DH_Griffel-Teaching the formation and solution of differential equations
    This paper raises many interesting questions about teaching the formation (and solution) of differential equations, i.e. modeling with differential equations.
    parasitesTopographypopulationepidemictraffic flowsocial interactionsfish weightarms race
    Potential Scenario
    197

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    65

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    2008-Huet-Deffuant-Differential Equation Models Derived from an Individual-Based Model Can Help to Understand Emergent Effects
    We study a model of primacy effect on individual's attitude. Typically, when receiving a strong negative feature first, the individual keeps a negative attitude whatever the number of moderate positive features it receives afterwards.
    agent-based modelprimacy effectinformation filteringaggregated modelcollectiveinteractionsdouble-modelling
    Potential Scenario
    144

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    59

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    2017-Agmour-EtAl-Optimization of the Two Fishermen's Profits Exploiting Three Competing Species Where Prices Depend on Harvest
    The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is...
    FishingharvestNash equilibriumoptimizeprofits
    Potential Scenario
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    2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy
    Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.
    cancertumor-inhibiting cytotoxic actiontumor-promoting inflammationimmune-induced tumor dormancytumor growth dynamics
    Potential Scenario
    127

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    47

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    1977-HI_Freedman-P_Whitman-Mathematical models of population interactions with dispersal
    A system of differential equations is proposed as a model of dispersion between two populations in habitats separated by a barrier.
    predatorbarriertwo populationstwo habitats
    Potential Scenario
    212

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    43

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    2014-Chivers-EtAl-Predator-prey systems depend on a prey refuge
    We present an agent-based model which does not require the factors or constraints of previous models to reproduce all six patterns in persistent populations.
    Individual & Agent Based Modelingpredator-preythink-pair-shareslynxrefugeprey switchingMustela-Clethrionomys systempatter oriented
    Article or Presentation
    104

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    56

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    0

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    2012-R_B_Ogunrinde-J_Sunday-On_some_models_based_on_second_order_differential_equations
    This paper presents some models based on second order differential equations. This is a very straightforward article with good explanations of modeling assumptions.
    combatcombat modelspecies interaction