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Sa' = (2 – x)(y – æ) %3| = y – 2x – 2 The system can be linearized at the critical point (-2,-2) to A where A = -4 4 -2 1 The eigenvalues are A1 = a, A2 = b, a < b (real), or d = a ± bi (complex) where |3D 3 a = 2 V7 b = 2 Based on this, the critical point is a(n) Asymptotically Stable v Spiral Point

Sa' = (2 – x)(y – æ) %3| = y – 2x – 2 The system can be linearized at the critical point (-2,-2) to A where A = -4 4 -2 1 The eigenvalues are A1 = a, A2 = b, a < b (real), or d = a ± bi (complex) where |3D 3 a = 2 V7 b = 2 Based on this, the critical point is a(n) Asymptotically Stable v Spiral Point

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Sx' = (2 – x)(y – x) - y' у — 2х — 2 The system can be linearized at the critical point (-2,-2) to = A where A = %D -4 4 -2 1 The eigenvalues are A1 a, X2 = b, a < b (real), or A = a ± bi (complex) where || a = V7 b = Based on this, the critical point is a(n) Asymptotically Stable v Spiral Point
Transcribed Image Text:Sx' = (2 – x)(y – x) - y' у — 2х — 2 The system can be linearized at the critical point (-2,-2) to = A where A = %D -4 4 -2 1 The eigenvalues are A1 a, X2 = b, a < b (real), or A = a ± bi (complex) where || a = V7 b = Based on this, the critical point is a(n) Asymptotically Stable v Spiral Point
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