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 to solve 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. Any help will be greatly appreciated.