Explain the determine red and the inf is here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn– kX+1 = Axn+ Bxp–k+CXp-1+Dxp-o+[dxn-k– ex-1(1)n= 0, 1,2, .....where the coefficients A, B, C, D, b, d, e e (0,00), whilek, 1 and o are positive integers. The initial conditionsX-g,..., X_1,..., X_ k, ..., X_1, Xo 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 byB=C= D=0, and k= 0, b is replaced by – b and in[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 [27] when6. 2 The local stability of the solutionsThe equilibrium point x 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 ž of Eq.(1) is given by|b(7)!![(A+B+C+D) – 1] (e – d)LetusnowintroduceacontinuousfunctionF: (0,00)4 -→ (0, 00) which is defined bybuiF(u0, U1, U2, U3) = Auo + Bun + Cu2+ Duz +(du – euz)'(8)provided du # euz. Consequently, we getƏF(x,x,X,X)= A= Po,Onee [(A+B+C+D) –1](e - d)ƏF(x,X,x,X)-.B-= P1,(9)ƏF(x,x,x,X)e[(A+B+C+D) –1](e - d)= C+= P2,ƏF(x,x,x,X)d u3D=P3,%3Dwhere et d. Thus, the linearized equation of Eq.(1) aboutx takes the formZn+1 - Pozn- P1Zn-k - P2 Zn-1- P3Zn-o = 0,(10)where po, P1, P2 and p3 are given by (9).

Name: Explain the determine red and the inf is here The objective of this ar
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Explain the determine red and the inf is here The objective of this article is to investigate somequalitative behavior of the solutions of the nonlineardifference equationbxn– kX+1 = Axn+ Bxp–k+CXp-1+Dxp-o+[dxn-k– ex-1(1)n= 0, 1,2, .....where the coe