Stability perilous

In the ascending bubble problem (Example 8), the requirement that the pressure at the surface should be positive rules out the dramatic behavior near the singular curve ( = but, by suitably defining the value of the derivative at the discontinuity, solution paths of perilous stability can be found4 (Cf. [312]). In Fig. 13, the broken line A = 0 is manifestly unstable. However, the broken line B = 0 can be reached in a finite time by a solution starting above A = 0 in the lower part of the phase plane and below A - 0 in the upper part. If the value at the singularity, B = 0, which is otherwise undefined, is correctly chosen, the solution turns and follows the path B = 0. In practice, it falls victim to the peril, even when stable. 

Taxonomic inflation and the stability of species lists the perils of ostrich s behaviour. Systematic Biology,... 

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