We saw before how a simple equation for the cytoplasmic concentration of calcium,

c, is dc dt

= 0.01 −

1.1c 2

0.32 + c 2

.

This is appropriate when the influx is constant and equal to 0.01 (with typical units of µM s−1

). However, in some cases, for some cells, the influx is a periodic function, which we can model approximately as a sine function. In this case dc dt

= 0.01(1 + Asin(t)) − 1.1c 2

0.32 + c 2

, c(0) = 0.1, where 0 ≤ A < 1.

a. Solve this equation numerically for A = 0, A = 0.2 and A =

0.9, plot the solutions, and comment on the differences.

b. For each value of A calculate the solution using the initial condition c(0) = 0.1 and the initial condition c(0) = 0.

Can you get a different solution as t → ∞ by choosing a different initial condition