In order to study this system, it is first necessary to discretise the equations.
For that, an Euler temporal scheme is used (it is the simplest one) to discretise the temporal derivatives:

Then, the following program is used to calculate x and y. The user has to give the parameters of the system, the initial conditions, the time step for the calculation and the number of iterations.
As results, the program plots x and y as functions of t on figure 1 (x is plotted in cyan and y is plotted in magenta) and y as a function of x on figure 2. It also plots the initial point in magenta and the critical point in cyan.

You can go to this program by clicking here.