Bifurcations: We would like to understand the behavior of the scalar iteration xn+1 = x+r (1)...

 

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Bifurcations: We would like to understand the behavior of the scalar iteration xn+1 = x+r (1) (a) Draw the bifurcation diagram showing the equilibria and periodic orbits of (1) for all r. (b) Use your diagram to find the region where (1) has a stable three periodic orbit. (c) Now answer (a) and (b) for the iteration xn+1 = (xn-sin(x))+r (2) Bifurcations: We would like to understand the behavior of the scalar iteration xn+1 = x+r (1) (a) Draw the bifurcation diagram showing the equilibria and periodic orbits of (1) for all r. (b) Use your diagram to find the region where (1) has a stable three periodic orbit. (c) Now answer (a) and (b) for the iteration xn+1 = (xn-sin(x))+r (2)