Originally Posted by

**Len** Is it possible to find a function g(y) (either continuous or discontinuous) such that the one-parameter family of differential equations

dy/dt=g(y)+a

satisfies both the following statements?

for all a<= -1, the differential equation has exactly one equilibrium point which is a sink.

for all >= 1, the differential equation has exactly three equalibria , two sources and one sink.

If so give a rough sketch, if not, why not?

I've sketched a ton of graphs now and can't get one to satisfy, also I have no idea how to explain then if it don't exist, why that is.

Thanks in advance.

Other than guessing is there a way for me to determine possible functions?