mu = 0.5;
a = 2;
w0 = 0.5;
x0 = 0.5;
y0 = 1;
tlim = 2000;

sol = 
      NDSolve[{x'[t]  ==  
            y[t], 
           y'[
              t]  ==  
            mu*(a^2 - (x[t])^2)*y[t] - (w0^2)*
                x[t], 
          x[0] == 
            x0, 
          y[0] == 
            y0}, 
      {y, x}, {t, tlim},  
        MaxSteps  ->  60000]

Plot[x[t] /. sol,  {t, 1500, 1600}];

ParametricPlot[{x[t], y[t]} /. sol, {t, 0, 100}];