Consider the nonlinear system....................................

Problem 4: Consider the nonlinear system :i: = mym(m2+5y2) 3'; = x+yy(rcg+yz) a) Classify the fixed point at the origin. b) Rewrite the system in polar coordinates (a: = 'rcos(9) and y = 'r sin(9)). 1 c) Prove that the system has a limit cycle in the annular region e