Difference between revisions of "Population growth models"
From JSXGraph Wiki
Jump to navigationJump to searchA WASSERMANN (talk | contribs) |
|||
(6 intermediate revisions by one other user not shown) | |||
Line 16: | Line 16: | ||
<jsxgraph height="500" width="600" board="board" box="box1"> | <jsxgraph height="500" width="600" board="board" box="box1"> | ||
− | brd = JXG.JSXGraph.initBoard('box1', { | + | var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.25, 12.5, 14.75, -12.5], axis:true}); |
− | var t = brd. | + | var t = brd.create('turtle',[4,3,70]); |
− | + | var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'}); | |
− | var s = brd. | + | var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'}); |
− | var alpha = brd. | + | var e = brd.create('functiongraph', [function(x){return s.Value()*Math.exp(alpha.Value()*x);}],{strokeColor:'red'}); |
− | var e = brd. | ||
t.hideTurtle(); | t.hideTurtle(); | ||
− | A = 5; | + | var A = 5; |
− | tau = 0.3; | + | var tau = 0.3; |
function clearturtle() { | function clearturtle() { | ||
Line 42: | Line 41: | ||
function loop() { | function loop() { | ||
− | var dy = alpha.Value()*t. | + | var dy = alpha.Value()*t.Y()*dx; // Exponential growth |
− | t.moveTo([dx+t. | + | t.moveTo([dx+t.X(),dy+t.Y()]); |
x += dx; | x += dx; | ||
if (x<20.0) { | if (x<20.0) { | ||
Line 57: | Line 56: | ||
===The JavaScript code=== | ===The JavaScript code=== | ||
− | <source lang=" | + | <source lang="javascript"> |
− | + | var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.25, 12.5, 14.75, -12.5], axis:true}); | |
− | brd = JXG.JSXGraph.initBoard('box1', { | + | var t = brd.create('turtle',[4,3,70]); |
− | var t = brd. | + | var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'}); |
− | + | var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'}); | |
− | var s = brd. | + | var e = brd.create('functiongraph', [function(x){return s.Value()*Math.exp(alpha.Value()*x);}],{strokeColor:'red'}); |
− | var alpha = brd. | ||
− | var e = brd. | ||
t.hideTurtle(); | t.hideTurtle(); | ||
+ | |||
+ | var A = 5; | ||
+ | var tau = 0.3; | ||
function clearturtle() { | function clearturtle() { | ||
Line 82: | Line 82: | ||
function loop() { | function loop() { | ||
− | var dy = alpha.Value()*t. | + | var dy = alpha.Value()*t.Y()*dx; // Exponential growth |
− | t.moveTo([dx+t. | + | t.moveTo([dx+t.X(),dy+t.Y()]); |
x += dx; | x += dx; | ||
if (x<20.0) { | if (x<20.0) { | ||
setTimeout(loop,10); | setTimeout(loop,10); | ||
} | } | ||
− | |||
} | } | ||
− | |||
</source> | </source> | ||
[[Category:Examples]] | [[Category:Examples]] | ||
[[Category:Turtle Graphics]] | [[Category:Turtle Graphics]] | ||
+ | [[Category:Calculus]] |
Latest revision as of 13:50, 8 June 2011
Exponential population growth model
In time [math] \Delta t[/math] the population consisting of [math]y[/math] elements grows by [math]\alpha\cdot y [/math] elements: [math] \Delta y = \alpha\cdot y\cdot \Delta t [/math], that is [math] \frac{\Delta y}{\Delta t} = \alpha\cdot y [/math].
With [math]\Delta t\to 0[/math] we get [math] \frac{d y}{d t} = \alpha\cdot y [/math], i.e. [math] y' = \alpha\cdot y [/math].
The initial population is [math]y(0)= s[/math].
The red line shows the exact solution of the differential equation [math]y(t)=s\cdot e^{\alpha t}[/math]. The blue line is the simulation with [math]\Delta t = 0.1[/math].
Other models
The JavaScript code
var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.25, 12.5, 14.75, -12.5], axis:true});
var t = brd.create('turtle',[4,3,70]);
var s = brd.create('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
var e = brd.create('functiongraph', [function(x){return s.Value()*Math.exp(alpha.Value()*x);}],{strokeColor:'red'});
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()*dx; // Exponential growth
t.moveTo([dx+t.X(),dy+t.Y()]);
x += dx;
if (x<20.0) {
setTimeout(loop,10);
}
}