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Ex Look at the fixed point (1,11 of [x = x-y lý -1-xy Jacobian: J(x, y) = (y _x) J(₁, 1) = (1 - 1) V₂ Eigenvalues: 1₁ = √₂ vectors: v₁ =(-1-1₂) -near fixed point looks like a linearized systen. +₂ = -√2 ✓₁₂ =(√²-1) => suddles linearization works

Ex Look at the fixed point (1,11 of [x = x-y lý -1-xy Jacobian: J(x, y) = (y _x) J(₁, 1) = (1 - 1) V₂ Eigenvalues: 1₁ = √₂ vectors: v₁ =(-1-1₂) -near fixed point looks like a linearized systen. +₂ = -√2 ✓₁₂ =(√²-1) => suddles linearization works

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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how do you find the vectors

Ex Look at the fixed point (1,11 of {&=x-xy X lý Jacobian: J(x, y) = (-y _x) J (₁, 1) = (₁ - 1) V₂ V₁ Eigenvalues: 1₁ = √2 vectors: v₁ = (-1-1₂) -near fixed point looks like a linearized systen x₂ = = √₂ => suddles linearization works √₂ V₂
Transcribed Image Text:Ex Look at the fixed point (1,11 of {&=x-xy X lý Jacobian: J(x, y) = (-y _x) J (₁, 1) = (₁ - 1) V₂ V₁ Eigenvalues: 1₁ = √2 vectors: v₁ = (-1-1₂) -near fixed point looks like a linearized systen x₂ = = √₂ => suddles linearization works √₂ V₂
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