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6. The nonlinear system y₁ = -9₁-92, y₂ = 9₁ +9₂, has steady states at (0,0), (1,-1), and (-1,1). Classify each steady state as a source (all eigenvalues have positive real part), sink (all eigenvalues have negative real part), saddle (one eigenvalue with positive real part and one with negative real part), or center (all eigenvalues purely imaginary).

6. The nonlinear system y₁ = -9₁-92, y₂ = 9₁ +9₂, has steady states at (0,0), (1,-1), and (-1,1). Classify each steady state as a source (all eigenvalues have positive real part), sink (all eigenvalues have negative real part), saddle (one eigenvalue with positive real part and one with negative real part), or center (all eigenvalues purely imaginary).

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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6. The nonlinear system y₁ = -y₁ - y2, y₂ = y₁ + y₂, has steady states at (0,0), (1, -1), and (-1,1). Classify each steady state as a source (all eigenvalues have positive real part), sink (all eigenvalues have negative real part), saddle (one eigenvalue with positive real part and one with negative real part), or center (all eigenvalues purely imaginary).
Transcribed Image Text:6. The nonlinear system y₁ = -y₁ - y2, y₂ = y₁ + y₂, has steady states at (0,0), (1, -1), and (-1,1). Classify each steady state as a source (all eigenvalues have positive real part), sink (all eigenvalues have negative real part), saddle (one eigenvalue with positive real part and one with negative real part), or center (all eigenvalues purely imaginary).
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