Find the equilibrium state of the dynamical system Xn+1 = 0.4xn+0.4yn, Yn+1 = 0.6xn +0.6yn- By equilibrium state, we mean find a vector vo (xo, yo) such that vn vo for all n. Of all possible answers for vo, give the unique answer which has entries that sum to 1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 23EQ
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Find the equilibrium state of the dynamical system
Xn+1
0.4xn + 0.4yn,
Yn+1
0.6xn + 0.6yn.
By equilibrium state, we mean find a vector v = (x0, Yo) such that in = vo for all n. Of all possible answers for vo, give the unique
answer which has entries that sum to 1.
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Transcribed Image Text:Find the equilibrium state of the dynamical system Xn+1 0.4xn + 0.4yn, Yn+1 0.6xn + 0.6yn. By equilibrium state, we mean find a vector v = (x0, Yo) such that in = vo for all n. Of all possible answers for vo, give the unique answer which has entries that sum to 1. ||
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