Модель Лотки

independent: {
    t: 0
},
dependent: {
    //x: [2, 2,   2, 2,   2, 2,   2, 2,   2, 0, 0,   0, 0,   0, 0,   0, 0,   0, 0.5, 1, 1.5, 2, 0, 0.5, 1, 1.5, 2],
    //y: [0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4,   4, 4,   4, 0, 0,   0, 0,   0]
	  x: [4, 4, 4, 4, 4,    0,    0,   0,   0, 0, 0, 0,   0.5],
      y: [0, 1, 2, 3, 3.5,  0.05, 0.1, 0.5, 1, 2, 3, 4,   4  ]
//    x: [0, 2],
//    y: [0, 4]
},
parameters: {
    k0: {
        min: 0.2,
        max: 4,
        value: 3
    },
    k1: {
        min: 1,
        max: 4,
        value: 2
    },
    k2: {
        min: 0.8,
        max: 3.7,
        value: 2
    }
},
derivatives: {
    dx_dt: 'k0 - k1 * x * y',
    dy_dt: 'k1 * x * y - k2 *y'
},
param_charts: [
  [{ 
    func:       'k2(x)', 
    equation:   'x*k1',
    swap_axes:  true,
    accuracy:   0.01,
    bounds:     { min: 0.01, max: 4 },
    options:    {lines: { lineWidth: 2} },
  }],
  [{ 
    func:       'k2(y)', 
    equation:   'k0 / y',
    solve:      true,
//limit_point_equations: {
//                'x(y)': '(k1 * y )'
//    },
    swap_axes:  true,
    accuracy:   0.01, 
    bounds:     { min: 0.01, max: 4 },
    options:    {lines: { lineWidth: 2} },
  }],
],
limit_points: {
    x: '[k2/k1]',
    y: '[k0/k2]',
},
solver: {
    step: 0.01,
    accuracy: 0.001,
    autostop: 10,
},
plot_options: {
    'x':  { min: 0, max: 4,},
	'y':  { min: 0, max: 4,}, 
    'k2': { min: 0.01, max: 4} 
},
init_hook: function() {
    var a = -calc.sys_state['k1']*calc.sys_state['k0']/calc.sys_state['k2'];
    var b = -calc.sys_state['k2'];
    var c = calc.sys_state['k1']*calc.sys_state['k0']/calc.sys_state['k2'];
    var d = 0;
    var s_2 = (a+d)/2;
    var delta = a*d-b*c;
    var s2_4 = s_2*s_2;
    if (s2_4 >= delta) {
        var l1 = '' + (s_2 - Math.sqrt(s2_4-delta)).toPrecision(3);
        var l2 = '' + (s_2 + Math.sqrt(s2_4-delta)).toPrecision(3);
    } else {
        var l1 = '' + s_2.toPrecision(3) + '+ ' + Math.sqrt(delta-s2_4).toPrecision(3) + ' \\cdot i';
        var l2 = '' + s_2.toPrecision(3) + '- ' + Math.sqrt(delta-s2_4).toPrecision(3) + ' \\cdot i';
    }
    $('trax_controller_postfix').innerText = '$$ \\begin{aligned} \\lambda_1 &= {'+l1+'} \\\\ \\lambda_2 &= {'+l2+'} \\end{aligned} $$';
    MathJax.Hub.Queue(["Typeset",MathJax.Hub,"trax_controller_postfix"]);
},

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