Система двух линейных дифференциальных уравнений

independent: {
    t: 0
},
dependent: {
    // x: [-1.5,-1.5,-1.5,-1.5,  1.5,1.5,1.5,1.5,  1.5,1.5,1.5,1.5,  -1.5,-1.5,-1.5,-1.5], 
    // y: [0.01,0.5,1,1.5,   0.01,0.5,1,1.5,    -0.01,-0.5,-1,-1.5,  -0.01,-0.5,-1,-1.5], 
	x: [-1,  1,  1,  -1], 
    y: [1,   1,    -1,  -1], 
},
parameters: {
    a: {
        min: -10,
        max: 10,
        value: -4
    },
    b: {
        min: -10,
        max: 10,
        value: -10
    },
	c: {
        min: -10,
        max: 10,
        value: 3
    },
	d: {
        min: -10,
        max: 10,
        value: -2
    },
},
derivatives: {
    dx_dt: 'a*x+b*y',
    dy_dt: 'c*x+d*y'
},

param_charts: [[
  { 
    func:       'Δ(σ)', 
    equation:   'σ*σ/4',
    swap_axes:  true,
    accuracy:   0.1,
    bounds:     { min: -20, max: 20 },
    options:    {lines: { lineWidth: 2}, color: 'blue' },
  },
  { 
    func:       'Δ(σ)', 
    equation:   '0',
    swap_axes:  true,
    bounds:     { min: -20, max: 20 },
    options:    {lines: { lineWidth: 2}, color: 'blue' },
  },
  { 
    func:       'σ(Δ)', 
    equation:   '0',
    bounds:     { min: 0, max: 200 },
    options:    {lines: { lineWidth: 2}, color: 'blue' },
  },
]],
limit_points: {
    σ: '[a+d]',
    Δ: '[a*d-b*c]',
},

plot_options: {
    'x': { min: -2, max: 2, min_stop: -4, max_stop: 4,},
	'y': { min: -2, max: 2, min_stop: -4, max_stop: 4,}, 
    'σ': { min: -20, max: 20, },
    'Δ': { min: -200, max: 200, },
},

plots: {
	'y(x)': true,
	'σ(Δ)': {set_variables: function(o) {
            //console.log('Δ =', o['Δ'], 'σ =', o['σ']);
            calc.lock = true;
            $('parameter_a').setValue(2*o['σ']/3);
            $('parameter_d').setValue(o['σ']-parseFloat($('parameter_a').getValue()));
            var bc = (parseFloat($('parameter_a').getValue())*parseFloat($('parameter_d').getValue()) - o['Δ']);
            $('parameter_b').setValue((bc == 0) ? 0 : (bc/Math.pow(Math.abs(bc),0.3)));
            calc.lock = false;
            $('parameter_c').setValue((parseFloat($('parameter_b').getValue()) == 0) ? 0 : (bc/parseFloat($('parameter_b').getValue())));
        }, shadowSize: 0},
    'x(t)': {set_variables: function(o) {for (i in o) delete o[i];}, shadowSize: 0},
	'y(t)': {set_variables: function(o) {for (i in o) delete o[i];}, shadowSize: 0},
},

init_hook: function() {
    var a = calc.sys_state['a'];
    var b = calc.sys_state['b'];
    var c = calc.sys_state['c'];
    var d = calc.sys_state['d'];
    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"]);
},

solver: {
    step: 0.01,
    accuracy: 0.1,
    autostop: 10,
}

\begin{cases} \frac{\displaystyle dx}{\displaystyle dt} = a x + b y \\ \frac{\displaystyle dy}{\displaystyle dt} = c x + d y \end{cases} $$ \sigma = a + d $$ $$ \Delta = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = a d - b c $$ $$ \lambda^2 - \sigma \lambda + \Delta = 0 $$ $$ \lambda_{1,2} = \frac{\sigma}{2} \pm \sqrt{\frac{\sigma^2}{4} - \Delta} $$

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