Let p and q be points in a 2- cycle for the logistic map. a) To show that if the cycle is superstable, then either p = 1 2 or q = 1 2 . b) To find out the value of r at which the logistic map has a super stable 2-cycle. Concept Introduction: ➢ Super stable points are the fixed points ( x * ) of an interval map T , when T(x * ) = 0 . ➢ The logistic map equation is f ( x ) = rx ( 1-x ) . ➢ The logistic equation is a different equation which is defined as the fixed point of the map in the interval [ 0 , 4 ] and also which determines the stability of the logistic map.

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Chapter 10.3, Problem 2E

Interpretation Introduction

Interpretation:

Let p and q be points in a 2- cycle for the logistic map.

a) To show that if the cycle is superstable, then either p =12 or q =12.

b) To find out the value of r at which the logistic map has a super stable 2-cycle.

Concept Introduction:

➢ Super stable points are the fixed points (x) of an interval map T, when T(x)=0.

➢ The logistic map equation is f(x) = rx(1-x).

➢ The logistic equation is a different equation which is defined as the fixed point of the map in the interval [0,4] and also which determines the stability of the logistic map.

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