Diffusion on a Directed Network, Grid VersionThis model demonstrates diffusion of a quantity through a directed network. The quantity moves among nodes in the network only along established, directed links between two nodes. The simple rules that drive this diffusion lead to interesting patterns related to the topology, density, and stability of the network. Furthermore, the model may be useful in understanding the basic properties of dynamic processes on networks, and provides a useful starting point for designing more complex and realistic network-based models. In this version the nodes are placed in a grid and connections are only possible with nearest neighbors. The neighborhood can be selected to be either Von Neumann or Moore. (see below). HOW IT WORKSIn each tick, each node shares some percentage (defined by the rate slider) of its "value" quantity with its neighbors in the network. Specifically, flow from node A to node B occurs only if there is a directed link from A to B and A has more value than B. The amount of flow is proportional to the difference between the value of A and the value of B, and the strength of the link from A to B. If a node has no outgoing links, then it doesn't share any of it's value; it just accumulates any that its neighbors have provided via incoming links. Note that because it is a directed network, node A may give value to node B even if node B doesn't give back. The size and color of each node shows how much "value" that node has, where the area of the node is proportional to its value. The strength of a link is indicated by its stroke width. During the simulation active links turn magenta with color intensity proportional to amount of flow. Hovering the mouse over either a node or link produces a tooltip respectively showing the current value of the node or flow through the link.The Total Value field demonstrates that value is conserved throughout the simulation. The Flow (Root Mean Square) field shows the root mean square of the flow between nodes at each time step. Note that this value decreases to 0. Click RESET to initialize the simulation. Double-clicking RESET also reconfigures the network. Then Network Type switch selects between the Von Neumann and Moore definitions of neighborhood. Moore neighborhoods permit links to any of a node's immediate neighbors including those on the diagonal, while Von Neumann neighborhoods eliminate those on the diagonal. With each reset a new network is configured with the probability of a link between a node pair given by the Connection Probability slider. From: Stonedahl, F. and Wilensky, U. (2008). NetLogo Diffusion on a Directed Network model. http://ccl.northwestern.edu/netlogo/models/DiffusiononaDirectedNetwork. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. |