For the following maps investigate all the critical points, calculating their position and stability properties as ,u is varied. Then sketch the...

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For the following maps investigate all the critical points, calculating theirposition and stability properties as ,u is varied. Then sketch the bifurcation diagram labelling any bifurcations by theirappropriate name and indicating the type of solutions your curves represent(stable or unstable critical or period—2 points ). Do not calculate the positionof any period-2 points, but do indicate how they would emerge and theirstability. (3“) $n+1 : 371;,(373; _ 4377: _ 1”)(b) mn+1 = mn(cos(:rn) + ,u), for Imn| < 7r/2