Consider i = x- y-x(x +5y), y x+y-y(x +y). a) Classify the fixed point at the...

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Consider i = x- y-x(x² +5y), y x+y-y(x +y). a) Classify the fixed point at the origin. b) Rewrite the system in polar coordinates, using ri = xx + yỷ and è = (xỷ - yi)/r. c) Determine the circle of maximum radius, ,, centered on the origin such that all trajectories have a radially outward component on it. d) Determine the circle of minimum radius, r,, centered on the origin such that all trajectories have a radially inward component on it. e) Prove that the system has a limit cycle somewhere in the trapping region Consider i = x- y-x(x² +5y), y x+y-y(x +y). a) Classify the fixed point at the origin. b) Rewrite the system in polar coordinates, using ri = xx + yỷ and è = (xỷ - yi)/r. c) Determine the circle of maximum radius, ,, centered on the origin such that all trajectories have a radially outward component on it. d) Determine the circle of minimum radius, r,, centered on the origin such that all trajectories have a radially inward component on it. e) Prove that the system has a limit cycle somewhere in the trapping region

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Solution Let and a Fixed points are given by and simultaneousl... View the full answer