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ompute the Feigenbaum delta from the logistic map. The logistic map is given by =+1 = µx;(1-x₂), and the Feigenbaum delta is defined as = lim 8, where 8, = n→∞0 mn-1-mn-2 mn-mn-1

ompute the Feigenbaum delta from the logistic map. The logistic map is given by =+1 = µx;(1-x₂), and the Feigenbaum delta is defined as = lim 8, where 8, = n→∞0 mn-1-mn-2 mn-mn-1

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Computation of the Feigenbaum delta Compute the Feigenbaum delta from the logistic map. The logistic map is given by Xi+= #X;(1 − xì), and the Feigenbaum delta is defined as mn-1-mn-2 mn-mn-1 and where m, is the value of μ for which xo = 1/2 is in the orbit of the period-N cycle with N = 2". Here is a resonable outline: Loop 1 Start at period-2" with n = 2, and increment n with each iteration Compute initial guess for m, using mn-1, mn-2 and 8-1. Loop 2 Iterate Newton's method, either a fixed number of times or until convergence Initialize logistic map Loop 3 Iterate the logistic map 2 times Computex and x Loop 3 (end) One step of Newton's method Loop 2 (end) Save m, and compute 8, 8 = lim 8, where 8₁= = n→∞0 Loop 1 (end) Grading will be done on the converged values of 8, up to n = 11. Set 8₁ = 5.
Transcribed Image Text:Computation of the Feigenbaum delta Compute the Feigenbaum delta from the logistic map. The logistic map is given by Xi+= #X;(1 − xì), and the Feigenbaum delta is defined as mn-1-mn-2 mn-mn-1 and where m, is the value of μ for which xo = 1/2 is in the orbit of the period-N cycle with N = 2". Here is a resonable outline: Loop 1 Start at period-2" with n = 2, and increment n with each iteration Compute initial guess for m, using mn-1, mn-2 and 8-1. Loop 2 Iterate Newton's method, either a fixed number of times or until convergence Initialize logistic map Loop 3 Iterate the logistic map 2 times Computex and x Loop 3 (end) One step of Newton's method Loop 2 (end) Save m, and compute 8, 8 = lim 8, where 8₁= = n→∞0 Loop 1 (end) Grading will be done on the converged values of 8, up to n = 11. Set 8₁ = 5.
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