R = 22.00;
x0 = 1.0;
y0 = 1.0;
z0 = 1.0;
x1 = 1.0;  y1 = 1.0;  z1 = 1.0001;
tlim = 2000;

sol = 
      NDSolve[{x'[t] == 
            3*(y[t] - 
                  x[t]), 
                 y'[t] == -1*x[t]*z[t] + R*x[t] - 
              y[t], 
                 z'[t] == 
            x[t]*y[t] - 
              z[t], 
                 x[
              0] == x0, y[0] == y0, 
          z[0] == 
            z0}, 
                   {z, 
          y, x}, {t, tlim}, 
        MaxSteps -> 200000]
sol2 = 
      NDSolve[{x'[t] == 
            3*(y[t] - 
                  x[t]), 
                 y'[t] == -1*x[t]*z[t] + R*x[t] - 
              y[t], 
                 z'[t] == 
            x[t]*y[t] - 
              z[t], 
                 x[
              0] == x1, y[0] == y1, 
          z[0] == 
            z1}, 
                   {z, 
          y, x}, {t, tlim}, MaxSteps -> 200000]

Plot[x[t] /. sol, {t, 0, 50}];
Plot[x[t] /. sol2, {t, 0, 50}];
Plot[{x[t] /. sol, x[t] /. sol2}, {t, 0, 50}];

Plot[
        Evaluate[x[t] /. sol] - Evaluate[x[t] /. sol2], {t, 0, 
          50}];

Plot[
        Log[Abs[Evaluate[x[t] /. sol] - Evaluate[x[t] /. sol2]]], {t, 0, 
          50}];

ParametricPlot[{x[t], z[t]} /. sol,  {t, 100, 200}];