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3.13 Consider the system * = 4x²y-f(x) (x² + 2y²-4) y = − 2x³-f₂(y) (x²+2y²-4) where the continuous functions f and f₂ have the same sign as their argument. Show that the system tends towards a limit cycle independent of the explicit expressions of f, and f2.

3.13 Consider the system * = 4x²y-f(x) (x² + 2y²-4) y = − 2x³-f₂(y) (x²+2y²-4) where the continuous functions f and f₂ have the same sign as their argument. Show that the system tends towards a limit cycle independent of the explicit expressions of f, and f2.

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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3.13 Consider the system * = 4x²y-f₁(x) (x² + 2y²-4) y = − 2x³-f₂(y) (x²+2y²-4) where the continuous functions f and f₂ have the same sign as their argument. Show that the system tends towards a limit cycle independent of the explicit expressions off, and f2.
Transcribed Image Text:3.13 Consider the system * = 4x²y-f₁(x) (x² + 2y²-4) y = − 2x³-f₂(y) (x²+2y²-4) where the continuous functions f and f₂ have the same sign as their argument. Show that the system tends towards a limit cycle independent of the explicit expressions off, and f2.
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