Show me the steps of determine red and the inf is here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn-kXn+1 = Axn+ Bx–k+Cxn-1+ Dxn-o+dxn-k– exŋ-n= 0,1,2,.....(1)where the coefficients A, B, C, D, b, d, e E (0,0), whilek, 1 and o are positive integers. The initial conditionsX_g,..., X_1,.., X_k, ….., X_1, X are arbitrary positive realnumbers such that k <1< 0. Note that the special casesof Eq.(1) have been studied in [1] when B=C= D=0,and k= 0,1= 1, b is replaced by – b and in [27] whenB=C= D=0, and k= 0, b is replaced by[33] when B = C = D = 0, 1= 0 and in [32] whenA=C= D=0, 1=0, b is replaced by – b.b and in%3| 2 The local stability of the solutionsThe equilibrium point of Eq.(1) is the positive solutionof the equationX= (A+B+C+D)x+(6)(d-e)x'where d + e. If [(A+B+C+ D) – 1] (e - d) > 0, thenthe only positive equilibrium point x of Eq.(1) is given bybX=[(A+B+C+D) – 1] (e – d)(7)LetusnowintroduceacontinuousfunctionF: (0, 00)4 -→ (0,00) which is defined bybuF(40, u1, U2, 13) = Auo + Bun +Cu2 + Du3 +(du– eu2-(8)provided dui # euz. Consequently, we getƏF(x,X,X,X)= A= Po,On ee [(A+B+C+D) –1](e – d)ƏF(x,X,x,X)-В-P1,%3|(9)e[(A+B+C+D) –1](e - d)ƏF(x,x,Xx,X)C+P2,ƏF(x,x,x,X)диз=D3DP3,where et d. Thus, the linearized equation of Eq.(1) aboutx takes the formZn+1 - Pozn- PıZn-k- P2Zn-1- P3Zn-o = 0,(10)%3Dwhere po, P1, P2 and p3 are given by (9).

Name: Show me the steps of determine red and the inf is here The objective o
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: Show me the steps of determine red and the inf is here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn-kXn+1 = Axn+ Bx–k+Cxn-1+ Dxn-o+dxn-k– exŋ-n= 0,1,2,.....(1)where t