(14 pts.) 3.) Logistic Map Consider the logistic map defined by the iterative equation In+1 = p in (1 - In) (1) where n

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14 Pts 3 Logistic Map Consider The Logistic Map Defined By The Iterative Equation In 1 P In 1 In 1 Where N 1 (64.29 KiB) Viewed 25 times

(14 pts.) 3.) Logistic Map Consider the logistic map defined by the iterative equation In+1 = p in (1 - In) (1) where n denotes the time step and p is the "growth” parameter. (a) Find the first-order fixpoint, 2*, defined by r = f(x) and determine the range of u values for which the fixpoint is stable. (hint consider small deviations from the fixpoint, f(x* + Ax) = f(x*) + f'2*)Ar; what condition should the derivative f'(x*) satisfy to render the fixpoint stable?) (b) The definition for second-order fixpoints is given by r = f(f(x)]. For p=3.3 it has the solutions r* = 0.479, 0.700,0.824. Sketch both sides of the equation, I = f(f(x)], graphically vs. x and determine whether the fixpoints are stable or unstable.