CODING IN PYTHON

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Already found the fixed points for (b):

(0,0), (2,0), (-1,3) and (3,-1)

The two curves, f(x,y)= 0 and g(x,y) = 0 are called the zero growth isoclines, or nullclines of the system.

Find the nullclines and fixed points of the following system of differential equations. dx dy = f(x, y) = x2 + xy 2x and = g(x, y) = xy2 + 3y dt dt (5) (a). plot the nullclines and the quiver plot for this system. (b). determine the fixed points of the system (there are 4 of them). (c). Determine the Jacobian matrix. (d). Evaluate the Jacobian matrix at all of the fixed points, and from this find the deter- minant and trace of the Jacobian at the fixed points. (e). Use the chart and/or table to determine the stability and behaviour of the solution close to the fixed points. (f). Choose an initial point close to each of the four fixed points (i.e. choose 4 initial points) and solve the equations at these points (i.e. you should produce 4 separate plots of x and y versust, one for each initial point)