Differential Equations: Problem Set 5

  1. (2.7) 2, 4, 8, 10

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

    1. \(x' = h - x^3\)

    2. \(x' = hx - x^2\)

    3. \(x' = (1-x)(x^2-h)\)

    4. \(x' = (x-\sqrt{h})(3-hx)\)

    5. \(x' = -(1+x)(x^2-h^2)\)

    6. \(x' = (x-1)(x-h)\)

    7. \(x'= x(1 - x) ^ 2 + \alpha\)