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For all positive values of a,b and c, determine the equilibrium points of the system * x1 = ax1 - x1x₂ x₂ = bx² - cx₂ X2 ac (0,0) saddle point; (√, a stable node if 8a ≤ c; (-√, a) stable focus if 8a > c; ac (0, 0) stable node; √, a) stable focus if 8a ≤ c; (-√, a) unstable focus if 8a > c; b ac (0,0) saddle point; (√, a) unstable node if 8a ≤ c; a) stable focus if 8a > c; " ac ac (0,0) stable node; (√, a) unstable focus if 8a ≤ c; (-√, a) unstable node if 8a > c; b

For all positive values of a,b and c, determine the equilibrium points of the system * x1 = ax1 - x1x₂ x₂ = bx² - cx₂ X2 ac (0,0) saddle point; (√, a stable node if 8a ≤ c; (-√, a) stable focus if 8a > c; ac (0, 0) stable node; √, a) stable focus if 8a ≤ c; (-√, a) unstable focus if 8a > c; b ac (0,0) saddle point; (√, a) unstable node if 8a ≤ c; a) stable focus if 8a > c; " ac ac (0,0) stable node; (√, a) unstable focus if 8a ≤ c; (-√, a) unstable node if 8a > c; b

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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* For all positive values of a,b and c, determine the equilibrium points of the system x₁ = ax₁ = ax1 - x1X₂ x₂ = bx² — cx₂ ac (0,0) saddle point; (√, a) stable node if 8a ≤ c; (-√, a) stable focus if 8a > c; ac ac ○ (0,0) stable node; (√, a) stable focus if 8a ≤ c; (-√√, a) unstable focus if 8a > c; ac ac ○ (0,0) saddle point; (√, a) unstable node if 8a ≤ c; (-√√, a) stable focus if 8a > c; ac ac ○ (0,0) stable node; (√, a) unstable focus if 8a ≤ c; (-√, a) unstable node if 8a > c; b
Transcribed Image Text:* For all positive values of a,b and c, determine the equilibrium points of the system x₁ = ax₁ = ax1 - x1X₂ x₂ = bx² — cx₂ ac (0,0) saddle point; (√, a) stable node if 8a ≤ c; (-√, a) stable focus if 8a > c; ac ac ○ (0,0) stable node; (√, a) stable focus if 8a ≤ c; (-√√, a) unstable focus if 8a > c; ac ac ○ (0,0) saddle point; (√, a) unstable node if 8a ≤ c; (-√√, a) stable focus if 8a > c; ac ac ○ (0,0) stable node; (√, a) unstable focus if 8a ≤ c; (-√, a) unstable node if 8a > c; b
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