2. Consider the system x' = x^3 +xy^2 −x −y, y' = x^2y + y^3 + x − y . (a) Transform the system into polar co-ordinates
Posted: Wed May 04, 2022 10:15 am
2. Consider the system x' = x^3 +xy^2 −x −y, y' = x^2y + y^3 + x
− y . (a) Transform the system into polar co-ordinates (r, θ) and
show that it has exactly one periodic orbit of constant radius. (b)
Classify the stability of the periodic orbit. [2 marks]
− y . (a) Transform the system into polar co-ordinates (r, θ) and
show that it has exactly one periodic orbit of constant radius. (b)
Classify the stability of the periodic orbit. [2 marks]