cacatoo
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Building, exploring, and sharing spatially structured models
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<!--
EXAMPLE FILE: Basic ODEs example
Odex.js is a library that can numerically solve ordinary differential equations. In
Cacatoo, you can add such a system to each grid point, and couple them by diffusion!
-->
<html>
<script src="../../dist/cacatoo.js"></script> <!-- Include cacatoo library (compiled with rollup) -->
<script src="../../lib/all.js"></script> <!-- Load other packages -->
<link rel="stylesheet" href="../../style/cacatoo.css"> <!-- Set style sheet -->
<script>
/*-----------------------Start user-defined code ---------------------*/
/*-----------------------Start user-defined code ---------------------*/
let sim;
function cacatoo() {
let config = {
title: "Numeric PDEs (ODEs in gridpoints)",
description: "Diffusion-coupled predator prey system (Lotka-Volterra)<br> <font size=1> A catastrophy kills some predators at time step 50.</font>",
maxtime: 1000000,
darkmode: true,
ncol: 64,
nrow: 64, // dimensions of the grid to build
wrap: [true, true], // Wrap boundary [COLS, ROWS]
scale: 3, // scale of the grid (nxn pixels per grid cell
}
sim = new Simulation(config)
sim.makeGridmodel("lotka");
sim.lotka.colourGradient('numpred', 100, [0, 0, 0], [240, 200, 0]) // Will contain the ODEs, and show the abundance of PREDATORS
sim.lotka.colourGradient('numprey', 100, [0, 0, 0], [148, 0, 211]) // Will contain the ODEs, and show the abundance of PREDATORS
sim.createDisplay_continuous({model:"lotka", property:"numpred", label:"Local predator density", // Createa a display for a continuous variable (ODE state for external resources)
minval:0, maxval:200})
sim.createDisplay_continuous({model:"lotka", property:"numprey", label:"Local prey density", // Createa a display for a continuous variable (ODE state for external resources)
minval:0, maxval:200})
// Define a basic Lotka Volterra ODE system
// dx/dt = a x - b x y
// dy/dt = c x y - d y
let LotkaVolterra = function (a, b, c, d) {
return function (x, y) {
return [
a * y[0] - b * y[0] * y[1], // y[0] is the prey which replicates with rate a, and gets consumed by the predator with rate b
c * y[0] * y[1] - d * y[1] // y[1] is the predator which consumes prey with rate c, dies naturally with rate d
]
}
}
// Configuration object with initial states, parameters, and diffusion rates
let ode_config = {
ode_name: "lotka",
init_states: [0, 0], // y[0] and y[1]
parameters: [3.5, 0.5, 0.5, 0.8], // a, b, c, d
diffusion_rates: [0.1, 0.01]
} // diffusion of y[0] and y[1]
// Attaches an ODE to all gridpoints with initial state = [0,0].
// By default, all ODEs are stored in an array in the grid point, but...
// If you want to access it by name, you can give a name as the final variable (here lotka)
sim.lotka.attachODE(LotkaVolterra, ode_config);
// Initialise the left 3 cols with predators and prey by setting the state via the named ODE 'lotka'
sim.lotka.grid[sim.lotka.nc / 2][sim.lotka.nr / 2].lotka.state = [10, 10]
// The nextState function has 3 steps: 1) ODE integration, 2) Diffusion, 3) Update what is displayed on the grid
sim.lotka.nextState = function (x, y) // Define the next-state function.
{
// 1) ODE integration
this.grid[x][y].lotka.solveTimestep(0.1, opt_pos = true)
// 3) Update how this GP is displayed
let prey = Math.max(0, this.grid[x][y].lotka.state[0]) // Amount of prey (continuous variable)
let pred = Math.max(0, this.grid[x][y].lotka.state[1]) // Amount of pred (continuous variable)
this.grid[x][y].numpred = Math.min(Math.floor(pred * 30), 200)
this.grid[x][y].numprey = Math.min(Math.floor(prey * 30), 200)
}
// Custom function to count the sum of predators / preys in the grid (used in update below)
sim.lotka.sumStates = function () {
let sumpred = 0
let sumprey = 0
for (let x = 0; x < this.nc; x++) // x are columns
for (let y = 0; y < this.nr; y++) // y are rows
{
sumprey += this.grid[x][y].lotka.state[0]
sumpred += this.grid[x][y].lotka.state[1]
}
return [sumpred, sumprey]
}
sim.lotka.update = function () {
if(sim.lotka.time==60){
for (let x = 0; x < this.nc; x++)
for (let y = 0; y < this.nr/2; y++)
this.grid[x][y].lotka.state[0] = 0
}
this.asynchronous() // For only solving the ODEs within grid points, asynchronous or synchronous is identical.
this.diffuseODEstates()
this.plotArray(["Predators", "Preys"],
[sim.lotka.sumStates()[0], sim.lotka.sumStates()[1]],
["gold", "#FF00AA"],
"Total predator/prey abundance")
this.plotArray(["Predators", "Preys"],
[this.grid[this.nc / 2][this.nr / 2].lotka.state[1],
this.grid[this.nc / 2][this.nr / 2].lotka.state[0],],
["gold", "#FF00AA"],
"ODE states in central grid point")
}
sim.addMovieButton(sim.lotka,"Local predator density",60)
sim.start()
}
/*-------------------------End user-defined code ---------------------*/
/*-------------------------End user-defined code ---------------------*/
</script>
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