Explain the determine red and the inf is here The main focus of this article is to discuss some qualitative behavior ofthe solutions of the nonlinear difference equationa1Ym-1+ a2Ym-2 + a3Ym-3 + a4Ym-4+ a5Ym-5Ym+1 =Aym+т 3D 0, 1, 2, ...,В1ут-1 + В2ут-2 + Взут-3 + Влут-4 + B5ут-5(1.1) Case 4. Let the function H(uo, ..., u5) is non-decreasing in uo,u1,u3 andnon-increasing in u2, u4, U5.Suppose that (d, D) is a solution of the systemD =H(D,D,d, D, d, d)andd = H(d, d, D, d, D, D).Then we geta1D+a2d + a3D+a4d + azda1d + a2D + azd + a4D + a5DD = AD+and d= Ad+B1D+ B2d + B3D+ B4d + BzdBid + B2D+ B3d + B4D+ B5D’or(a1 + a3) D+ (a2 + a4 + a5) d(B1 + B3) D + (B2 + B4 + B5) d(a1 + a3) d + (a2+ a4 + az) D(B1 + B3) d + (82 + B4 + B5) DD(1 – A) =and d(1– A) =-From which we have+ a3) D+ (a2 + a4 + az) d-(1 – A) (B1 + B3) D² = (1 – A) (B2 + B4 + B5) Dd(5.41)and(a1 + a3) d+ (a2 + a4 + a5) D-(1 – A) (B1 + B3) ď² = (1 – A) (82 + B4 + B5) Dd(5.42)From (5.41) and (5.42), we obtain(d – D) {[(a1 + a3) – (a2 + a4 + a5)] – (1 – A) (B1 + B3) (d + D)} = 0.(5.43)Since A < 1 and (a2 + a4 + a5) > (a1 + a3), we deduce from (5.43) thatD = d. It follows by Theorem 2, that ỹ of Eq.(1.1) is a global attractor.It follows by Theorem 2, that ỹ of Eq.(1.1) is a global attractor and theproof is now completed.

Name: Explain the determine red and the inf is here The main focus of this a
Uploaded: 2024-03-20T07:07:37.000Z
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Description: Explain the determine red and the inf is here The main focus of this article is to discuss some qualitative behavior ofthe solutions of the nonlinear difference equationa1Ym-1+ a2Ym-2 + a3Ym-3 + a4Ym-4+ a5Ym-5Ym+1 =Aym+т 3D 0, 1, 2, ...,В1ут-1 + В2ут