Autocatalytic process - Revision history

A WASSERMANN at 07:55, 16 July 2019

2019-07-16T07:55:16Z

← Older revision		Revision as of 07:55, 16 July 2019
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	The initial population is <math>y(0)= s</math>, <math>A := 5</math>.		The initial population is <math>y(0)= s</math>, <math>A := 5</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 11:58, 7 June 2011

2011-06-07T11:58:36Z

← Older revision		Revision as of 11:58, 7 June 2011
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	===The JavaScript code===		===The JavaScript code===
	<source lang="javascript">		<source lang="javascript">
	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, 12.5, 14.5, -12.5], keepaspectratio: false, axis:true});
	var t = brd.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);

Michael at 11:58, 7 June 2011

2011-06-07T11:58:01Z

← Older revision		Revision as of 11:58, 7 June 2011
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	</html>		</html>

	<jsxgraph height="500" width="600" ~~board="board"~~ box="box1">		<jsxgraph height="500" width="600" 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, 12.5, 14.5, -12.5], keepaspectratio: false, axis:true});
	var t = brd.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);

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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', {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.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);
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	}		}
	}		}
	~~</jsxgraph>~~
	</source>		</source>

A WASSERMANN at 20:46, 29 September 2010

2010-09-29T20:46:29Z

← Older revision		Revision as of 20:46, 29 September 2010
Line 15:		Line 15:

	<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.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);

Line 24:		Line 24:
	t.hideTurtle();		t.hideTurtle();

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

	function clearturtle() {		function clearturtle() {
Line 57:		Line 57:
	<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.create('turtle',[4,3,70]);		var t = brd.create('turtle',[4,3,70]);

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

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

	function clearturtle() {		function clearturtle() {

A WASSERMANN at 20:42, 29 September 2010

2010-09-29T20:42:29Z

← Older revision		Revision as of 20:42, 29 September 2010
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', {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.create('turtle',[4,3,70]);

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

	t.hideTurtle();		t.hideTurtle();
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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});		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],[-5,0.5,5]], {name:'s'});		var s = brd.create('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.create('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'});		//var e = brd.create('functiongraph', [function(x){return s.Value()Math.exp(alpha.Value()x);}],{strokeColor:'red'});

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

A WASSERMANN at 14:50, 14 July 2010

2010-07-14T14:50:55Z

← Older revision		Revision as of 14:50, 14 July 2010
Line 94:		Line 94:

	[[Category:Examples]]		[[Category:Examples]]
			[[Category:Calculus]]
	[[Category:Turtle Graphics]]		[[Category:Turtle Graphics]]

A WASSERMANN at 07:51, 23 June 2009

2009-06-23T07:51:22Z

← Older revision		Revision as of 07:51, 23 June 2009
Line 41:		Line 41:

	function loop() {		function loop() {
	var dy = alpha.Value()t.~~pos[1]~~(A-t.~~pos[1]~~)*dx; // Autocatalytic process		var dy = alpha.Value()t.Y()(A-t.Y())*dx; // Autocatalytic process
	t.moveTo([dx+t.~~pos[0]~~,dy+t.~~pos[1]~~]);		t.moveTo([dx+t.X(),dy+t.Y()]);
	x += dx;		x += dx;
	if (x<20.0) {		if (x<20.0) {
Line 83:		Line 83:

	function loop() {		function loop() {
	var dy = alpha.Value()t.~~pos[1]~~(A-t.~~pos[1]~~)*dx; // Autocatalytic process		var dy = alpha.Value()t.Y()(A-t.Y())*dx; // Autocatalytic process
	t.moveTo([dx+t.~~pos[0]~~,dy+t.~~pos[1]~~]);		t.moveTo([dx+t.X(),dy+t.Y()]);
	x += dx;		x += dx;
	if (x<20.0) {		if (x<20.0) {

A WASSERMANN at 07:45, 23 June 2009

2009-06-23T07:45:10Z

← Older revision		Revision as of 07:45, 23 June 2009
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	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();

	A = 5;		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](A-t.pos[1])*~~delta~~; // Autocatalytic process		var dy = alpha.Value()t.pos[1](A-t.pos[1])*dx; // Autocatalytic process
	t.moveTo([~~delta~~+t.pos[0],y+t.pos[1]]);		t.moveTo([dx+t.pos[0],dy+t.pos[1]]);
	x += ~~delta~~;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);

A WASSERMANN at 07:44, 23 June 2009

2009-06-23T07:44:28Z

← Older revision		Revision as of 07:44, 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();
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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](A-t.pos[1])*~~delta~~; // Autocatalytic process		var dy = alpha.Value()t.pos[1](A-t.pos[1])*dx; // Autocatalytic process
	t.moveTo([~~delta~~+t.pos[0],y+t.pos[1]]);		t.moveTo([dx+t.pos[0],dy+t.pos[1]]);
	x += ~~delta~~;		x += dx;
	if (x<20.0) {		if (x<20.0) {
	setTimeout(loop,10);		setTimeout(loop,10);

A WASSERMANN: /* Autocatalytic population growth model */

2009-05-12T18:14:18Z

Autocatalytic population growth model

← Older revision		Revision as of 18:14, 12 May 2009
Line 1:		Line 1:
	===Autocatalytic population growth model===		===Autocatalytic population growth model===
	In time <math> \Delta t</math> the population grows by <math>\alpha\cdot y \cdot(A-y)</math> elements:		Here, in time <math> \Delta t</math> the population grows by <math>\alpha\cdot y \cdot(A-y)</math> elements:
	<math> \Delta y = \alpha\cdot y\cdot \Delta t \cdot(A-y)</math>, that is		<math> \Delta y = \alpha\cdot y\cdot \Delta t \cdot(A-y)</math>, that is
	<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y \cdot(A-y)</math>.		<math> \frac{\Delta y}{\Delta t} = \alpha\cdot y \cdot(A-y)</math>.

	With <math>\Delta \to 0</math> we get		With <math>\Delta t\to 0</math> we get
	<math> \frac{d y}{d t} = \alpha\cdot y \cdot (A-y) </math>, i.e. <math> y' = \alpha\cdot y \cdot (A-y) </math>.		<math> \frac{d y}{d t} = \alpha\cdot y \cdot (A-y) </math>, i.e. <math> y' = \alpha\cdot y \cdot (A-y) </math>.