Logistic process

From JSXGraph Wiki

Logistic population growth model

In time Δt the population grows by elements: , that is .

With we get , i.e. .

The initial population is y(0) = s, τ: = 0.3.

The blue line is the simulation with Δt = 0.1.

Other models

• Population growth models
• Autocatalytic process

The JavaScript code

var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.5, 11.5, 14.5, -11.5], axis:true});
var t = brd.create('turtle',[4,3,70]);
var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});
 
t.hideTurtle();
 
var A = 5;
var tau = 0.3;
 
function clearturtle() {
  t.cs();
  t.ht();
}
 
function run() {
  t.setPos(0,s.Value());
  t.setPenSize(4);
  dx = 0.1; // global
  x = 0.0;  // global
  loop();
}
 
function loop() {
  var dy = (alpha.Value()*t.Y()-tau*t.Y()*t.Y())*dx; // Logistic process
  t.moveTo([dx+t.X(),dy+t.Y()]);
  x += dx;
  if (x<20.0) {
     setTimeout(loop,10);
  }
}