This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 6. Discuss symmetry and reversibility properties (if any) of the equations in problems 3 and 4 7. Consider the following dynamical system in the plane that depends on the real parameter μ . ˙ x =x ( x 2 + y 2μ )y ( x 2 + y 2 ) ˙ y =y ( x 2 + y 2μ ) + x ( x 2 + y 2 ) (a) Show that the system has a periodic orbit for μ > 0. 2 (b) Is it stable? 8. Discuss the evolution of the phase portraits in the preceding question as μ varies from negative to positive. 9. Consider the system ¨ x = αxx 3 . Study the evolution of the phase portraits of this system as α varies from negative to positive. 10. Add a ﬁxed amount of dissipation to the preceding system and repeat the question. Include a study of symmetries as well....
View
Full Document
 Fall '09
 Marsden
 phase portrait, Dynamical systems

Click to edit the document details