{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw6 - Hint for 4.3.7 For this problem the bifurcations...

This preview shows page 1. Sign up to view the full content.

Math 454 Problem Set #6 Fall 2008 Sect. 1 Due Tuesday, 10/7, at the beginning of class. Reminder. You are encouraged to work together on homework problems. However, the final write- up must be your own. You will be quizzed on some of these problems, so be sure you can do all the problems without help. Read: Sects. 4.5, 5.1-2 Problems - Sect. 4.3 #2, 7*, 8* (bonus) - Sect. 4.5 #1(a-c) * The vector fields in 4.3.7 & 8 can have “singularities,” that is, places where the vector field is infinite. Singularities are like fixed points: they can be stable or unstable, they can change stability, and they can be created or destroyed in bifurcations.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Hint for 4.3.7: For this problem, the bifurcations occur at μ = 1 , , and -1. Plot phase portraits for μ > 1 , < μ < 1 ,-1 < μ < , and μ <-1 , then sketch a bifurcation diagram that includes both ﬁxed points and singularities (no need to distinguish ﬁxed points from singularities, but be careful to label their stability). What type of bifurcations do you see? Hint for 4.3.8: The bifurcations occur at μ = 1 and -1. Draw phase portraits for μ > 1 ,-1 < μ < 1 , and μ <-1 , then put the ﬁxed points and the singularities into a bifurcation diagram. What do you see?...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern