Category Archives: interacting particle systems

3.11 the Schelling model implemented as an interacting particle system

This model demonstrates how the Schelling model can be implemented as an interacting particle system exclusion process.

The video shows the emergence of segregated regions of different types (red and blue) separated by the vacant (grey) state.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.9 voter model with dispersal and mutation

This model implements a simple voter model with two non-local processes. One admits succession at a distance, while the other (mutation) allows the appearance of completely new states in the lattice.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.8 simple voter model

This model is an implementation of a simple voter model.

The video demonstrates how regions of each original class or type develop and persist.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.7 Simple rock – scissors – paper IPS model

This model is an implementation of a rock – scissors – paper succession model.

In the video you should be able to see how red invades yellow invades blue invades red, in a cyclic relationship.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.6 grass – bush – trees IPS succession model

This model is an implementation of the simple grass – bush – trees model of

Durrett R and Swindle G 1991 Are there bushes in a forest?. Stochastic Processes and their Applications, 37, 19–31.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.5 Competing contact processes

This is an implementation of competing contact processes in two dimensions, including an option for one of the processes to spread over long distances. Models of this kind are discussed in

Durrett R and Levin SA 1994b Stochastic spatial models: a user’s guide to ecological applications. Philosophical Transactions of the Royal Society of London. Series B. 343, 329-350.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.

3.4 Basic two dimensional contact process

This is an implementation of a basic contact process in two dimensions. The contact process is one of the simplest possible interacting particle systems. It is discussed in some detail in

Durrett R and Levin SA 1994b Stochastic spatial models: a user’s guide to ecological applications. Philosophical Transactions of the Royal Society of London. Series B. 343, 329-350.

Click on the image to download and save the model NetLogo file. You will need to install NetLogo to run this file.