Cubic Map Problem 10.3.6 (Cubic map) Consider the cubic map X = f(x,), where f(x,) = rx, - x a) Find the fixed points. F

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Cubic Map Problem 10 3 6 Cubic Map Consider The Cubic Map X F X Where F X Rx X A Find The Fixed Points F 1 (28.24 KiB) Viewed 28 times

Cubic Map Problem 10.3.6 (Cubic map) Consider the cubic map X = f(x,), where f(x,) = rx, - x a) Find the fixed points. For which values of r do they exist? For which values are they stable? b) To find the 2-cycles of the map, suppose that f(p) = q and f(q) = p. Show that P.q are roots of the equation x(r? -r + 1)(x? -r-1)(x* -rx + 1) = 0 and use this to find all the 2-cycles. c) Determine the stability of the 2-cycles as a function of r. d) Plot a partial bifurcation diagram, based on the information obtained.