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) ifaa +B+- < 1.(5)Proof: Suppose that ( and n are real numbers and assume that F: S,n13 IS, nl is a function defined byF(r, y, z) = Br + ay +bz+cThenƏF(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. ThenBx + ax +- x| (x – TO)bx +c[-(1-a - B)a +(a - 0) s- (1-a-8-:)*<0ax- a -bxIf 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 equationXn+1 = Bxn-i+axn-k +axn-tn = 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

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Answered: Now, we can see that the function F(x,…

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

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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