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Simulation de phénomènes collectifs

Concevoir et programmer une simulation de phénomène collectif

Mise en oeuvre avec Netlogo

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Thèmes

Ø Propagation de maladie dans une population• Avec ou sans vaccin

Ø Théorie de l’evolution• Les plus adaptés finissent par être les plus nombreux

Ø Dynamique de population• Lapin, renard, herbe etc..

Ø …

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Etapes

Ø Choisir un thème (!)• Définir la question qui sera répondue• Faire des hypotheses (choix de modélisation)

Ø Proposer une première modélisation simplissime• Objectif prendre en main l’outil et cibler les comportements de

base• Evaluer sa réponse à la question

Ø Incrémentalement, complexifier le modèle pour mieuxrépondre à la question

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Netlogo platform

Ø http://ccl.northwestern.edu/netlogo/Ø Interpreted languageØ Dedicated to complex system simulationØ Individual centered (logo turtle)Ø Fonctionnalities

• 2D (/3D) model • GUI builder with slider, button, reporter,,• Graphs wizard (various possbilities: min,max, min, …)• Concurrent programming

Ø Free (possibility of online (simplified) version)

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Netlogo

Ø Components of a model • Environnment :

– Discrete 2D torous grid– Cell = patch

• attributes, visual aspect (color)

• Turtles (agents) micro level– Situated (x,y + orientation) in environment– Actions: movements, modification of patch/other agents

• Observation macro level– Global variables– Global processing (init., patch evolution, stats, …)– Execution management

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Component of the netlogo platform

Ø Graphical interface: • Visual view of the model

– Agent positions• User interface

– Parameter, execution(start …)

• Observing– Graphs, reporters

Ø « execution oriented »

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Ø Code • Observing code• Turtles code• Variables

Ø « Programmingoriented »

Component of the netlogo platform

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Netlogo

Ø Numerous (!) documented examplesØ Very easy to learn (even for non programmers)Ø Conection to JAVA, scala code ; applet possibilitiesØ Parameters space exploration Ø Fast (!)butØ Be caution with syntax (eg: dont forget white space)Ø Not so easy when advanced programming concepts are

needed

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Toy exampleopinion dynamics

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Opinion dynamics(a first glance on a well known model)

G. DEFFUANT, G., NEAU, D., AMBLARD, F. and WEISBUCH, G. 2000.

Mixing beliefs among interacting agents. Advances in Complex Systems, 3, 87-98.

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Basic principles

Ø Agents • Have an opinion

Ø Interaction• 2 agents with close opinions will move their opinions closer

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Model

Ø Agent i defined by it opinion • Float xi

Ø Close opinions ó• | xi-xj| < d

Ø Opinions move closer• Xi = xi + k (xj-xi)• And symetrically forxj

• K : convergence factor (between 0 and0.5)

Ø Mathematical model is possible

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Numerical simulation

Ø Initialisation• Create N agents• Provide themwith an initial (random) opinion

Ø Simulation (loop)• Pick two agents• If they are “close” then update

• Demo with Netlogo

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Variations

Ø Interaction• 2 agents with close opinions will move their opinions closer

Ø Interaction• 2 agents with close opinions will move their opinions closer

Move closer instead of « fusion »

Influence ???

What if distance is not symetrical ?

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A small demo

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Other works

Ø And agents are not sincere ?Ø Reputational effect, preferences falsification

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A step-by-step example

Ø Dynamics of opinion• Rather than meeting "at random", agents travel and "discuss" with

their neighbours

Ø Steps Random movement• Meet/convince each other• Visualization

• ExtensionS

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InitializationØ Primitive

• Clear-all• Crt/create-turtles number [ commands ]

• Reset-ticksØ Interface

• Setup/ go buttons• Slider nb turtles

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Traveling

Ø Primitive• forward number• random-float number

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Dynamics of opinion

Ø Individual model• "attribute" opinion • (initially random)

Kesako?

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Dynamics of opinion

Ø Individual model• "attribute" Opinion • (initially random)

Ø Collective properties• Threshold Factor (slider)

Ø Dynamics• To know if agents meet each other• Update of opinion

Ø Graphical interface• Each step, opinion diagram

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Code

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Ø One-of • Takes at random one from a list

Ø Turtles-on• Set of turtles in a patch set

Ø Neighbors• Patches around the current patch

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Dynamics of opinion

Ø Individual model• "attribute" Opinion • (initially random)

Ø Collective properties• Threshold Factor (slider)

Ø Dynamics• To know if agents meet each other• Update of opinion

Ø Graphical interface• Each step, opinion diagram

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Extension

Ø There are three categories of populations• Each with a different threshold• Each with a different factor

Ø New agents can be created during the simulationØ agents move in groups according to their opinion (+/-

close)

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A tutorial on netlogo

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A step by step example

Ø Rabbit grass: population dynamics

• Rabbit are wandering in a “garden”• Grass growths regularly• Rabbits can eat grass and reproduce• If rabbits cannot eat for a while, they die

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MAS modeling with netlogo

Ø EnvironmentØ AgentsØ DynamicsØ System loop/initialization

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Environment modeling

Ø 2D grids of patchesØ Patch

• Featured by grass quantity (the resource)Ø Dynamics

• Grass grows each cycle• Grass can be eaten (by rabbits) and decreases

Ø Initially: random quantity

Ø Display• According to grass quantity: the more grass the greener

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Modeling of agents (turtles)

Ø Internal state• Energy

Ø Behavior• Random movements• Eat grass• Live (spent energy, die or reproduce)

Ø Initially• Random position and energy

Ø Display (opt.)• Use/design a specific icon (turtle shape editor, ….)

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Modeling of dynamics

Ø Each cycle• Ask every rabbit to:

– Move– Eat– Live (spend energy, reproduce or die)

• Ask every patch to:– grow grass

• Provide some statistical information

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Basic elements in netlogo

Ø Creating turtles at random positionsØ Making them move

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Makes turtles move randomly

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Basic elements in netlogo

Ø Creating turtlesØ Making them moveØ Defining procedures/global variablesØ Creating a basic graphical interfaceØ Simulating a model

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Ø Clearing the world (reset all)Ø Putting grass

• define patch feature• Initialize the feature

Ø Making grass growing• Define a method to make grass grow

Ø Provide a visual display

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Ø Putting all together• Merge initializations• Let’s rabbits eat, spend energy and die/reproduce• Provide a “loop” function

Ø Providing statistics

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initialization

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Procedure in code

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Rabbits behavior

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To be continued …

Ø See rabbit grass weeds in netlogo library