# The origin is either a nodal or spiral sink all

This preview shows pages 24–25. Sign up to view the full content.

part. The origin is either a nodal or spiral sink. All trajectories remain bounded but do not approach the origin, and occurs when eigenvalues are pure imaginary. The origin is a center. Some trajectories, and possibly all trajectories except x = 0 , tend to infinity. This occurs when at least one of the eigenvalues is positive or has a positive real part. The origin is a nodal source, a spiral source, or a saddle point.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Summary Table The following table summarizes the information we have derived about our 2 x 2 system x ' = Ax , as well as the stability of the equilibrium solution x = 0 . Eigenvalues Type of Critical Point Stability 0 2 1 r r Node Unstable 0 2 1 < < r r Node Asymptotically Stable 1 2 0 r r < < Saddle Point Unstable 0 2 1 = r r Proper or Improper Node Unstable 0 2 1 < = r r Proper or Improper Node Asymptotically Stable μ λ i r r ± = 2 1 , Spiral Point 0 λ Unstable 0 < λ Asymptotically Stable μ μ i r i r - = = 2 1 , Center Stable
This is the end of the preview. Sign up to access the rest of the 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