Differential Equations: Problem Set 5

(2.7) 2, 4, 8, 10

For each of the following, find the equilibria, determine their stability and produce a bifurcation diagram. Include appropriate sentences summarizing the various cases.

1. x′=h−x3

2. x′=hx−x2

3. x′=(1−x)(x2−h)

4. x′=(x−√h)(3−hx)

5. x′=−(1+x)(x2−h2)

6. x′=(x−1)(x−h)

7. x′=x(1−x)2+α