Question 1 For the systems below, find and classify the critical points using linear stability method, also indicate if the equilibria are stable, asymptotically stable, or unstable. (i) dx =x(1-x+y), dy dt dt =y(1 -y+x). dy (ii) =-a+ ray - c' dt dt = y(1 - y), where r > 1. du du (iii dt = 1(0 - 1), =4- 12 - v2. dt Question 2 Graph the nullclines, sketch the direction fields, and investigate the stability of the steady states for the following systems. Note: The nullclines may not be straight lines. (a) = 2r (1 -=) -xy, dt dy = it 3y (1 - ") - 2xy. (b) = 2x (1 it dy 9 = y( -y ) - xy. dt