A system of differential equations is a collection of differential equations such as
\left{\begin{align} \frac{dx}{dt} = F(x, y) \\ \frac{dy}{dt} = G(x, y) \end{align}\right} \hspace{0.5cm}\text{where} \hspace{0.5cm} x(t), y(t)The solution to this system of differential equations is consists of a pair of functions and that satisfies both equations simultaneously for every over some time interval. Plotting the points in the -plane we define a solution curve called the trajectory of the system. The -plane in which the trajectories reside is the phase plane.
Equilibrium Rest Points
If there exist trajectories in the phase-plane that move away from certain equilibrium- or rest points of the differential system, these points are considered unstable equilibria
Asymptotical Limit Shapes
The behavior of a system trajectoy can also asymptotically approach a limiting shape such as a circle which encloses the equilibria that are being approached. Such is then called a limit circle.