Consider the system where r² = x² + y². J = -y+x(r4-3r²+1), \ ý = x + y(r²¹ - 3r²+1), (a) Use the Poincaré-Bendixson Theorem to show that there is a periodic orbot in the annular region A₁ = {(x, y)|1 < √√x² + y² <2}. (b) Show that the origin is an unstable focus for this system and use the Poincaré- Bendixson Theorem to show that there is periodic orbit in the annular region A₂ = {(x, y)le < √² + y² < 1}, where 0 < € <<< 1.
Consider the system where r² = x² + y². J = -y+x(r4-3r²+1), \ ý = x + y(r²¹ - 3r²+1), (a) Use the Poincaré-Bendixson Theorem to show that there is a periodic orbot in the annular region A₁ = {(x, y)|1 < √√x² + y² <2}. (b) Show that the origin is an unstable focus for this system and use the Poincaré- Bendixson Theorem to show that there is periodic orbit in the annular region A₂ = {(x, y)le < √² + y² < 1}, where 0 < € <<< 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 32E
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