Bifurcations and Differential Equations

6. Now consider the differential equation dy/dt = y2 - m. Draw the phase lines for m equal to 0, 1/4, 1, and 4, side by side from left to right. Then sketch a "continuum of phase lines" for all real values of m greater than or equal to zero (such a "continuum of phase lines" is called a bifurcation diagram .)













What do you notice?



7. Draw several solution curves in the t-y plane separately for each of the four discrete phase lines listed above. What is the qualitative relationship between your sketches here and the "continuum of phase lines" in 6?