Show me the steps of determine blue and information is here THEOREM 3.2. The equilibrium point T1 is a global attractor of difference equation (1) ifB+a < 1.(6)Proof: Suppose that ( and n are real numbers and assume that g : 5,n]3 → 5,nl is a function defined byg(u, υ , w ) βυ αυ +awbw+cThenag(u, v, w)dvдg(и, v, w)= B,ас= a and g(u, v, w)(bw+c)² ·duNow, we can see that the function g(u, v, w) increasing in u, v and w.Let (m, M) be a solution of the system M9(М, М, М) and m —g(m, m, m). Then from Eq. (1), wesee thataMamМ — ВМ + аM +m = Bm + am +bM + c'bm + cthusb(la – B)M² – c(1 – a – B)M6(la – B)m? – c(1- a - B)mаМ,am. Our goal is to obtain some qualitative behavior of the positive solutions of the difference equationaIn-tIn+1 = Bxn-it axn-k +n = 0, 1,(1)bxn-t+c'where the parameters B, a, a, b and c are positive real numbers and the initial conditions x-s, -s+1,..., x-1,xo are positive real numbers where s =max{l, k, t}.

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Now, we can see that the function g(u, v, w) increasing in u, v and w. Let (m, M) be a solution of the system M = g(M, M, M) and m = g(m, m, m). Then from Eq. (1), we see that aM am М — ВМ +аМ + Вт + am + m = bM + c' bm + c thus b(la – B)M² – c(1 - a - B)M b(la – B)m? – c(1 - a - B)m аМ, am.

Now, we can see that the function g(u, v, w) increasing in u, v and w. Let (m, M) be a solution of the system M = g(M, M, M) and m = g(m, m, m). Then from Eq. (1), we see that aM am М — ВМ +аМ + Вт + am + m = bM + c' bm + c thus b(la – B)M² – c(1 - a - B)M b(la – B)m? – c(1 - a - B)m аМ, am.

Algebra and Trigonometry (6th Edition)

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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