EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 10.2, Problem 3E
Interpretation Introduction

Conclusion:

Compute the orbit diagram for the logistic map.

Concept Introduction:

  • ➢ Logistic map: A logistic map is defined as the polynomial map of the degree two and chaotic behavior can arise from a non-linear dynamic equation.

  • ➢ The expression for the logistic map is, xn+1= r xn(1-xn) here, xn is the number between zeros and r is the intrinsic growth rate.

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1. Give a subset that satisfies all the following properties simultaneously: Subspace Convex set Affine set Balanced set Symmetric set Hyperspace Hyperplane 2. Give a subset that satisfies some of the conditions mentioned in (1) but not all, with examples. 3. Provide a mathematical example (not just an explanation) of the union of two balanced sets that is not balanced. 4. What is the precise mathematical condition for the union of two hyperspaces to also be a hyperspace? Provide a proof. edited 9:11
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