I have Lotka Volterra Equations where the prey equation is modified. The Equations are

    x'[t]=a*x[t]*(1-x[t]/k)-b*x[t]*y[t]
    y'[t]=-c*y[t]+d*x[t]*y[t]

To plot the limit cycles, i used `NDSolve` to solve the coupled nonlinear differential equations for x[t] and y[t]. I then used `ParametricPlot` to plot for `x[t]` and `y[t]` with respect to `t`, but I'm not getting appropriate limit cycles.

I did a steady state analysis of the equations and got certain conditions on the value of `a`, `b`, `c`, `d` and `k`. The equation has a non-trivial steady state, at $(x,y)=(c/d,(a/b)-(ac/bdk))$. The commands are:

    Equations = {x'[t] == ax[t]*(1 - x[t]/k) - bx[t]*y[t], x[0] == 2, y[0] == 1, y'[t] == -cy[t] + dx[t]*y[t]}; 
    s = NDSolve[{Equations}, {x, y}, {t, 0, time}];
    ParametricPlot[Evaluate[{x[t], y[t]} /. s], {t, 0, 30}] 

For the value of `a = 2; b = 1; c = 2.5; d = 1.2; k = 2.8`, I'm supposed to get a unstable spiral. But instead, the trajectory approaches the steady state of $(x,y) = (2.08333 , 0.511905)$.


Any help will be greatly appreciated.