3. Consider the nonlinear system da dt dy = -2x + y = -4y + 2xy...

 

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3. Consider the nonlinear system da dt dy = -2x + y = -4y + 2xy dt (a) Sketch the phase portrait and identify the fixed points. (b) Show that this is a gradient system and find the potential function V (x, y). (c) Argue that if (co, yo) is in the square S = {(x, y): -1 < x, y < 1} and V (ro, yo) < 1, then the solution curve starting at (zo, yo) will approach the origin. 3. Consider the nonlinear system da dt dy = -2x + y = -4y + 2xy dt (a) Sketch the phase portrait and identify the fixed points. (b) Show that this is a gradient system and find the potential function V (x, y). (c) Argue that if (co, yo) is in the square S = {(x, y): -1 < x, y < 1} and V (ro, yo) < 1, then the solution curve starting at (zo, yo) will approach the origin.