Question

Determine the bifurcation value(s) for the one-parameter family

Answer 1

Let's say we have a one parameter family:

dydt=y2+kdydt=y2+k

I want to find the bifurcation value. What does this mean?

It seems like I need to set dy/dt = 0 and then solve for k, but then I get a negative square root:

0=y2+k0=y2+k

y2=−ky2=−k

y=sqrt(−k)y=sqrt(−k)

or

k=−y2