Homework Help is Here – Start Your Trial Now!
Math
Algebra
Now, we can see that the function F(x, y, z) increasing in x, y and z. Then Bx + ax + - 1 (x - To) bx +c < [-(1-a- 8) z + ax (x- 0) < -(1-a-8-)-²

Now, we can see that the function F(x, y, z) increasing in x, y and z. Then Bx + ax + - 1 (x - To) bx +c < [-(1-a- 8) z + ax (x- 0) < -(1-a-8-)-²

Linear Algebra: A Modern Introduction
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
See similar textbooks
icon
Related questions
Question

Show me the steps of determine red and information is here step by step 

THEOREM 3.1. The equilibrium point To is a global attractor of difference equation (1) if a a +B+- < 1. (5) Proof: Suppose that ( and n are real numbers and assume that F: S,n13 IS, nl is a function defined by F(r, y, z) = Br + ay + bz+c Then ƏF(r, y, z) = 3, aF(r, y, 2) = a and OF(x, y, z) ас %3D (bz+c)? • Now, we can see that the function F(x, y, z) increasing in x, y and z. Then Bx + ax + - x| (x – TO) bx +c [-(1-a - B)a + (a - 0) s- (1-a-8-:)*<0 ax - a - bx If a +B+ < 1, then F(x, y, z) satisfies the negative feedback property [F(x, x, x) - ] (x- To) < 0, for To = 0.
Transcribed Image Text:THEOREM 3.1. The equilibrium point To is a global attractor of difference equation (1) if a a +B+- < 1. (5) Proof: Suppose that ( and n are real numbers and assume that F: S,n13 IS, nl is a function defined by F(r, y, z) = Br + ay + bz+c Then ƏF(r, y, z) = 3, aF(r, y, 2) = a and OF(x, y, z) ас %3D (bz+c)? • Now, we can see that the function F(x, y, z) increasing in x, y and z. Then Bx + ax + - x| (x – TO) bx +c [-(1-a - B)a + (a - 0) s- (1-a-8-:)*<0 ax - a - bx If a +B+ < 1, then F(x, y, z) satisfies the negative feedback property [F(x, x, x) - ] (x- To) < 0, for To = 0.
Our goal is to obtain some qualitative behavior of the positive solutions of the difference equation Xn+1 = Bxn-i+axn-k + axn-t n = 0, 1, ..., (1) bxn-t+c' where the parameters 3, a, a, b and c are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, xo are positive real numbers where s = max{1, k, t}. .D TT T T
Transcribed Image Text:Our goal is to obtain some qualitative behavior of the positive solutions of the difference equation Xn+1 = Bxn-i+axn-k + axn-t n = 0, 1, ..., (1) bxn-t+c' where the parameters 3, a, a, b and c are positive real numbers and the initial conditions x-s, x-s+1, ..., x-1, xo are positive real numbers where s = max{1, k, t}. .D TT T T
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer