1. The problem statement, all variables and given/known data Find the fixed points and classify them using linear analysis. Then sketch the nullclines, the vector field, and a plausible phase portrait. dx/dt = x(x-y), dy/dt = y(2x-y) 2. Relevant equations 3. The attempt at a solution f1(x,y) = x(x-y) x-nullcline: x(x-y) = 0 [itex]\Rightarrow[/itex] x = 0 f2(x,y) = y(2x-y) y-nullcline: y(2x-y) = 0 [itex]\Rightarrow[/itex] y = 0 Fixed point: (0,0) J(x,y) = (2x-y -x ) (2y 2x-2y) Therefore, J(0,0) = (0 0) (0 0) Thus, 0 = |J(0,0) - λI| = (-λ)(-λ) = λ2 = 0 [itex]\Rightarrow[/itex] λ1,2 = 0 ___________________________________________________________________ Now this is where I get stuck; I have no idea where to go from here when λ1 = λ2 = 0. I would really appreciate at least a little nudge in the right direction. Thank you.