Explore BrainMass
Share

Quadratic Maps Two-Cycles

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Show that the 2-cycle of the quadratic map is stable if 3/4<5/4. The quadratic map is x(n+1)=x(n)^2-c.

© BrainMass Inc. brainmass.com March 21, 2019, 10:36 am ad1c9bdddf
https://brainmass.com/math/derivatives/quadratic-maps-two-cycles-19170

Solution Preview

Please see attached file

Show that the 2-cycle of the quadratic map is stable if ¾ < c < 5/4. The quadratic map is x = x - c.

Solution: A 2-cycle exists if and only if there are two points and such that and . Equivalently, such a must satisfy , where . Hence is a fixed point of the ...

Solution Summary

The expert shows that the two-cycle of a quadratic map is stable if 3.4<5/4. The quadratic map functions are provided.

$2.19