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7 Consider the system x = =μx1-x2 ×₂ = x₁ + (4+1)×2 a) Show that (x,,x2)=(0,0) is the unique fixed-point of the system for all μER. 6) show that if 2μ+1 20, then (x,,x2)=(0,0) d is an asymptotically stable fixed-point. What happens when 2μ+1=0.

7 Consider the system x = =μx1-x2 ×₂ = x₁ + (4+1)×2 a) Show that (x,,x2)=(0,0) is the unique fixed-point of the system for all μER. 6) show that if 2μ+1 20, then (x,,x2)=(0,0) d is an asymptotically stable fixed-point. What happens when 2μ+1=0.

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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7 Consider the system x = =μx1-x2 ×₂ = x₁ + (4+1)×2 a) Show that (x,,x2)=(0,0) is the unique fixed-point of the system for all μER. 6) show that if 2μ+1 20, then (x,,x2)=(0,0) d is an asymptotically stable fixed-point. What happens when 2μ+1=0.
Transcribed Image Text:7 Consider the system x = =μx1-x2 ×₂ = x₁ + (4+1)×2 a) Show that (x,,x2)=(0,0) is the unique fixed-point of the system for all μER. 6) show that if 2μ+1 20, then (x,,x2)=(0,0) d is an asymptotically stable fixed-point. What happens when 2μ+1=0.
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