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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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 Spring '08
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