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Stable Focus

  To analyze the dynamics in the vicinity of the fixed point b we need to find the eigenvalues and eigenvectors of

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The eigenvalues of tex2html_wrap_inline15488 are

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where

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The fixed point b is a stable focus since the real parts of the eigenvalues are negative. This focus represents the constant intensity output of a laser, and the oscillation about this steady state is the ringing a laser initially experiences when it is turned on.

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Figure 4.17: Phase portrait for the laser rate equation.

The global phase portrait, pieced together from local information about the fixed points, is pictured in Figure 4.17.



Nicholas B. Tufillaro
Mon Mar 3 01:58:02 PST 1997