I have problems identifying the invariant sets of the following dynamical system. Let $\mu,\lambda,\alpha>0$ and lets focus our attention in the first quadrant, $x\geq 0, y\geq 0$ . $$\dot x = (1-y-\lambda x)x$$ $$\dot y = \alpha(1-x-\mu y)y$$
I know that the invariant set has to be the points where the trajectories stays where they begin. Thats why I know that the origin in this case is invariant. Now, other possible invariant sets are the points where we have an equilibrium, and in this case the points are $(0,0),(0,\frac{1}{\mu}),(\frac{1}{\lambda}0,)$ and if $(1-y-\lambda x), (1-y-\lambda x)$ intersect, we have $(\frac{1-\mu}{1-\lambda},\frac{1-\lambda}{1-\mu\lambda})$. Since I know that in all of those points, $\dot x$ and $\dot y$ are $0$, then what is the difference between invariant sets and fixed/equilibrium points? What would be all the invariant sets for this system?
Thanks so much :)