recall that u v consider the equation u a a v b b 0

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lues of , the roots are distinct, with one always negative. When , the roots have opposite signs. Hence the equilibrium point is a saddle. For the case , the roots are both negative, and the equilibrium point is a stable node. represents a transition from saddle to node. When , both roots are equal. For the case , the roots are complex conjugates, with negative real part. Hence the equilibrium point is a stable spiral. ________________________________________________________________________ page 393 —————————————————————————— CHAPTER 7. —— 19. The characteristic equation for the system is given by The roots are First note that the roots are complex when . We also find that when , the equilibrium point is a stable spiral. For the case , the equilibrium point is a center. When , the equilibrium point is an unstable spiral. For all other cases, the roots are real. When , the roots have opposite signs, with the equilibrium point being a...
View Full Document

Ask a homework question - tutors are online