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

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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...
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