flaming . . . you know how to get started with this? Let me give you some tips:
(1) Write the system as pretty as possible else some will not want to bother interpreting your writing. Here's what I did after a lot of processing:
See. That makes a lot of difference. Now shake and bake:
(a) Find the equilibrium points by setting the right side to zero. Flat out, I'm not going to do that by hand (just use Solve in Mathematica). Maybe you want to. Anyway they are:
(b) Linearize it by calculating the Jacobian matrix for each equilibrium point.
(c) Find the eigenvalues for each matrix.
(d) Based on the sign of the eigenvalues, determine the stability of the equilibrium points.
(e) Finally, rely heavily on Mathematica to plot the results. You can use VectorFieldPlot to draw the vector field easily. Use NDSolve to solve the system for some select initial conditions and superimpose these solutions in the vector field to illustrate how the solutions follow the field. Use Point to show where the eq. points are and by plotting a lot of solutions, show how the solutions are affected by the stability of the eq. points.