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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
how do you find the
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2edb8953-1391-481e-8461-1fc64ce8e7a2%2F20dc268c-1e34-4bde-b4fe-9332d022bc3c%2F0uvyq9x_processed.png&w=3840&q=75)
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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