Logistic process - Revision history

A WASSERMANN at 07:54, 16 July 2019

2019-07-16T07:54:33Z

← Older revision		Revision as of 07:54, 16 July 2019
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	The initial population is <math>y(0)= s</math>, <math>\tau:=0.3</math>.		The initial population is <math>y(0)= s</math>, <math>\tau:=0.3</math>.

	~~The blue line is the simulation with <math>\Delta t = 0.1</math>.~~
	<html>		<html>
	<form><input type="button" value="clear and run" onClick="clearturtle();run()"></form>		<form><input type="button" value="clear and run" onClick="clearturtle();run()"></form>

Michael at 08:46, 8 June 2011

2011-06-08T08:46:48Z

← Older revision		Revision as of 08:46, 8 June 2011
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	<jsxgraph height="500" width="600" board="board" box="box1">		<jsxgraph height="500" width="600" board="board" box="box1">
	var brd = JXG.JSXGraph.initBoard('box1', {~~originX~~: 10, ~~originY: 250~~, ~~unitX: 40~~, ~~unitY: 20~~, axis:true});		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 t = brd.create('turtle',[4,3,70]);
	var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
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	===The JavaScript code===		===The JavaScript code===
	<source lang="~~xml">~~		<source lang="javascript">
	~~<jsxgraph height="500" width="600" board="board" box="box1~~">		var brd = JXG.JSXGraph.initBoard('box1', {boundingbox: [-0.5, 11.5, 14.5, -11.5], axis:true});
	var brd = JXG.JSXGraph.initBoard('box1', {~~originX~~: 10, ~~originY: 250~~, ~~unitX: 40~~, ~~unitY: 20~~, axis:true});
	var t = brd.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
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	}		}
	}		}
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 20:45, 29 September 2010

2010-09-29T20:45:57Z

← Older revision		Revision as of 20:45, 29 September 2010
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	<jsxgraph height="500" width="600" board="board" box="box1">		<jsxgraph height="500" width="600" board="board" box="box1">
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		var brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.~~createElement~~('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.~~createElement~~('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
	var alpha = brd.~~createElement~~('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});		var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});

	t.hideTurtle();		t.hideTurtle();

	A = 5;		var A = 5;
	tau = 0.3;		var tau = 0.3;

	function clearturtle() {		function clearturtle() {
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	<source lang="xml">		<source lang="xml">
	<jsxgraph height="500" width="600" board="board" box="box1">		<jsxgraph height="500" width="600" board="board" box="box1">
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		var brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.~~createElement~~('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
	var s = brd.~~createElement~~('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});		var s = brd.create('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
	var alpha = brd.~~createElement~~('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});		var alpha = brd.create('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});

	t.hideTurtle();		t.hideTurtle();

	A = 5;		var A = 5;
	tau = 0.3;		var tau = 0.3;

	function clearturtle() {		function clearturtle() {

A WASSERMANN at 14:51, 14 July 2010

2010-07-14T14:51:32Z

← Older revision		Revision as of 14:51, 14 July 2010
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	[[Category:Examples]]		[[Category:Examples]]
			[[Category:Calculus]]
	[[Category:Turtle Graphics]]		[[Category:Turtle Graphics]]

A WASSERMANN at 17:00, 3 August 2009

2009-08-03T17:00:50Z

← Older revision		Revision as of 17:00, 3 August 2009
Line 58:		Line 58:
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.createElement('turtle',[4,3,70]);		var t = brd.createElement('turtle',[4,3,70]);
	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});

	t.hideTurtle();		t.hideTurtle();

A WASSERMANN at 17:00, 3 August 2009

2009-08-03T17:00:15Z

← Older revision		Revision as of 17:00, 3 August 2009
Line 17:		Line 17:
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.createElement('turtle',[4,3,70]);		var t = brd.createElement('turtle',[4,3,70]);
	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[0,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.9,2]], {name:'α'});

	t.hideTurtle();		t.hideTurtle();

A WASSERMANN at 07:48, 23 June 2009

2009-06-23T07:48:39Z

← Older revision		Revision as of 07:48, 23 June 2009
Line 17:		Line 17:
	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.createElement('turtle',[4,3,70]);		var t = brd.createElement('turtle',[4,3,70]);

	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	~~//var e = brd.createElement('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});~~

	t.hideTurtle();		t.hideTurtle();
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	brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});		brd = JXG.JSXGraph.initBoard('box1', {originX: 10, originY: 250, unitX: 40, unitY: 20, axis:true});
	var t = brd.createElement('turtle',[4,3,70]);		var t = brd.createElement('turtle',[4,3,70]);

	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	~~var e = brd.createElement('functiongraph', [function(x){return s.X()Math.exp(alpha.X()x);}],{strokeColor:'red'});~~

	t.hideTurtle();		t.hideTurtle();

	tau = 0.3;		A = 5;
			tau = 0.3;

	function clearturtle() {		function clearturtle() {
	t.cs();		t.cs();
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	function run() {		function run() {
	t.setPos(0,s.X());		t.setPos(0,s.Value());
	t.setPenSize(4);		t.setPenSize(4);
	~~delta~~ = 0.1; // global		dx = 0.1; // global
	x = 0.0; // global		x = 0.0; // global
	loop();		loop();
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	function loop() {		function loop() {
	var y = (alpha.X()t.~~pos[1]~~-taut.~~pos[1]~~t.~~pos[1]~~)~~delta~~; // Logistic process		var dy = (alpha.Value()t.Y()-taut.Y()t.Y())dx; // Logistic process
	t.moveTo([~~delta~~+t.~~pos[0]~~,y+t.~~pos[1]~~]);		t.moveTo([dx+t.X(),dy+t.Y()]);
	x += ~~delta~~;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);

A WASSERMANN at 07:47, 23 June 2009

2009-06-23T07:47:12Z

← Older revision		Revision as of 07:47, 23 June 2009
Line 42:		Line 42:
	function loop() {		function loop() {
	var dy = (alpha.Value()t.Y()-taut.Y()t.Y())dx; // Logistic process		var dy = (alpha.Value()t.Y()-taut.Y()t.Y())dx; // Logistic process
	t.moveTo([dx+t.X(),dy+t.Y());		t.moveTo([dx+t.X(),dy+t.Y()]);
	x += dx;		x += dx;
	if (x<20.0) {		if (x<20.0) {

A WASSERMANN at 07:46, 23 June 2009

2009-06-23T07:46:56Z

← Older revision		Revision as of 07:46, 23 June 2009
Line 20:		Line 20:
	var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});		var s = brd.createElement('slider', [[0,-5], [10,-5],[-5,0.5,5]], {name:'s'});
	var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});		var alpha = brd.createElement('slider', [[0,-6], [10,-6],[-1,0.2,2]], {name:'α'});
	//var e = brd.createElement('functiongraph', [function(x){return s.X()Math.exp(alpha.X()x);}],{strokeColor:'red'});		//var e = brd.createElement('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

	t.hideTurtle();		t.hideTurtle();
Line 33:		Line 33:

	function run() {		function run() {
	t.setPos(0,s.X());		t.setPos(0,s.Value());
	t.setPenSize(4);		t.setPenSize(4);
	~~delta~~ = 0.1; // global		dx = 0.1; // global
	x = 0.0; // global		x = 0.0; // global
	loop();		loop();
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	function loop() {		function loop() {
	var y = (alpha.X()t.~~pos[1]~~-taut.~~pos[1]~~t.~~pos[1]~~)~~delta~~; // Logistic process		var dy = (alpha.Value()t.Y()-taut.Y()t.Y())dx; // Logistic process
	t.moveTo([~~delta~~+t.~~pos[0]~~,y+t.~~pos[1]]~~);		t.moveTo([dx+t.X(),dy+t.Y());
	x += ~~delta~~;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);

A WASSERMANN: /* Logistic population growth model */

2009-05-12T18:15:27Z

Logistic population growth model

← Older revision		Revision as of 18:15, 12 May 2009
Line 1:		Line 1:
	===Logistic population growth model===		===Logistic population growth model===
	In time <math> \Delta t</math> the population grows by <math>\alpha\cdot y -\tau\cdot y^2)</math> elements:		In time <math> \Delta t</math> the population grows by <math>\alpha\cdot y -\tau\cdot y^2</math> elements:
	<math> \Delta y = (\alpha\cdot y- \tau\cdot y^2)\cdot \Delta t</math>, that is		<math> \Delta y = (\alpha\cdot y- \tau\cdot y^2)\cdot \Delta t</math>, that is
	<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y -\tau\cdot y^2</math>.		<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y -\tau\cdot y^2</math>.