Answered: Find all parameters a ∈ (0, 4] for…

Find all parameters a ∈ (0, 4] for which the logistic family ga(x) = ax(1 − x) has an attracting 2-cycle. Conclude that there is in fact a period-doubling bifurcation at a = 3.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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Question

Find all parameters a ∈ (0, 4] for which the logistic family g_a(x) = ax(1 − x) has an attracting 2-cycle. Conclude that there is in fact a period-doubling bifurcation at a = 3.

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