Find all limit cycles of system x₁ =−x₂ + x₁(1-x² - x²) (2 - x² - x²), x₂ = X₁ + X₂(1 − x² − x²)(2 − x² − x²), - determine their stability, and then sketch the phase portrait of the system.
Find all limit cycles of system x₁ =−x₂ + x₁(1-x² - x²) (2 - x² - x²), x₂ = X₁ + X₂(1 − x² − x²)(2 − x² − x²), - determine their stability, and then sketch the phase portrait of the system.
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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Transcribed Image Text:Find all limit cycles of system
x₁ = x₂ +
x₁(1-x²-x²)(2-x²-x²),
x₂ = x₁ + x₂(1-x²-x²) (2 - x²-x²),
determine their stability, and then sketch the phase portrait of the system.
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