I know it has been ages with no answer, but I just got STACK working again on my main sandbox, and I took a look at this. It appears to me the problem is with you start and finish. This worked for me. At least it produced a nice graph.
Please not that to keep them visible, I had to ad a space between the brackets. [ [ and [ ]. The code is:
[ [jsxgraph width='500px' height='500px'] ]
// boundingbox:[left, top, right, bottom]
var brd = JXG.JSXGraph.initBoard(divid, {axis: true, boundingbox: [-0.5, 4, 5, -0.5], showCopyright: false, shownavigation: false});
var xaxis = brd.create('text', [4.5,-0.3, "U"]);
var yaxis = brd.create('text', [-0.4,3.5, "V"]);
// create nullcline dummies
var l1p1 = brd.create('point',[4,2], {name:'',face:'<>',strokeColor:'green',size:2});
var l1p2 = brd.create('point',[4,2.5], {name:'',face:'<>',strokeColor:'green',size:2});
var l1 = brd.create('line',[l1p1,l1p2], {straightFirst:false, straightLast:false,strokeColor:'green',strokeWidth:2,dash:1});
var l2p1 = brd.create('point',[4.5,2], {name:'',face:'<>',strokeColor:'green',size:2});
var l2p2 = brd.create('point',[4.5,2.5], {name:'',face:'<>',strokeColor:'green',size:2});
var l2 = brd.create('line',[l2p1,l2p2], {straightFirst:false, straightLast:false,strokeColor:'green',strokeWidth:2,dash:1});
var l3p1 = brd.create('point',[4,1], {name:'',face:'<>',strokeColor:'green',size:2});
var l3p2 = brd.create('point',[4,1.5], {name:'',face:'<>',strokeColor:'green',size:2});
var l3 = brd.create('line',[l3p1,l3p2], {straightFirst:false, straightLast:false,strokeColor:'green',strokeWidth:2,dash:1});
var l4p1 = brd.create('point',[4.5,1], {name:'',face:'<>',strokeColor:'green',size:2});
var l4p2 = brd.create('point',[4.5,1.5], {name:'',face:'<>',strokeColor:'green',size:2});
var l4 = brd.create('line',[l4p1,l4p2], {straightFirst:false, straightLast:false,strokeColor:'green',strokeWidth:2,dash:1});
var button1 = brd.create('button', [3.5, 3.5, 'Calculate trajectory', function() {clearturtle(); run();}], {});
var ic = brd.create('point',[1,1],{size:4,name:'(U(0), V(0))'});
var UV = brd.create('turtle',[1,2],{strokeColor:'blue',strokeWidth:3});
var b = 3;
var a = 4;
var t = 0;
var U = ic.X();
var V = ic.Y();
var delta = 0.01;
UV.hideTurtle();
function clearturtle() {
UV.cs();
UV.hideTurtle();
}
function run() {
UV.setPos(ic.X(),ic.Y());
U = ic.X();
V = ic.Y();
t = 0;
loop();
}
function loop() {
// define RHSs of the equation
var dU = delta*(2*U*(1-U/b)-U*V);
var dV = delta*(U*V-a*V);
U = U+dU;
V = V+dV;
UV.moveTo([U,V]);
t += delta;
if (t<100.0) {
active = setTimeout(loop,10);
}
}
brd.unsuspendupdate();
[ [/jsxgraph] ]