(a) Consider the blood cell iterative equation (12.6). Assuming that b = 1.1 × 106, r = 8, and s = 16, show that there are (i) two stable and one unstable fixed points of period one when a = 0.2, and (ii) two unstable and one stable fixed point of period one when a = 0.3.

(b) Assume that σ = 0.5, β = 0.3, γ = 0.2, λ = 0.2, m = 1 in the economic model (12.7). Show that there is a stable fixed point of period one at x1,2 = 0.263 when B = 1, and an unstable fixed point of period one at x1,2 = 0.873 when B = 3.3.

(c) Show that the inverse map of equation (12.8) is given by En+1 =

(En − A)

B exp



−i

φ −

CB2

(B2 + |En − A|2)



.

(d) Consider the neuromodule model (12.10). Assume that θ1 = −2, θ2 = 3, w11 = −20, w12 = 6, and w21 = −6. Show that there is one fixed point of period one approximately at (−1.280, 1.695), and that it is a saddle point.