Stability
Quiz: Stability.
.
In the autonomous equation y = f (y) , where f (y) has the graph shown,
descibe the rightmost critical point.
ẏ
ẏ = f (y)
-1
1
y
Choices:
a) stable
b) unstable
c) semistable
c) can’t tell, could be any of them
Answer: Unstable. This is evident from the phase line.
y
unstable 1
stable 0
unstable -1
The phase line shows that the critical point at y = 1 is unstable.
MIT OpenCourseWare
http://ocw.mit.edu
18.03SC Differential Equations��
Fall 2011 ��
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.