第 1 題
Suppose a population of bacteria doubles every hour, but that 1.0 × 106 individuals are removed before reproduction to be converted into valuable biological by-products. Suppose the population begins with b0 = 3.0 × 106 bacteria.
- Find the population after 1, 2, and 3 hours.
- Write the discrete-time dynamical system.
第 2 題
In one simple scenario, mutations occur in only one direction (wild type tum into mutants but not vice versa), but wild type and mutants have different levels of per capita production. Suppose that a fraction 0.1 of wild type mutate each generation, but that each wild type individual produces 2.0 offspring while each mutant produces only 1.5 offspring. In each case, find the following.
- The number of wild-type bacteria that mutate.
- The number of wild-type bacteria and the number of mutants after mutation.
- The number of wild-type bacteria and the number of mutant after reproduction.
- The total number of bacteria after mutation and reproduction.
- The fraction of mutants after mutation and reproduction.
(Begin with 1.0 × 106 wild type and 1.0 × 105 mutants.)
第 3 題
again a lung that has a volume of 6.0 L and that replaces 0.6 L each
breath with ambient air. Suppose that we are tracking oxygen, with an ambient concentration
of 21%. Assume that the actual oxygen concentration in exhaled air is approximately 15%.
What fraction of oxygen is in fact absorbed?
第 4 題
The model describing the dynamics of the concentration of medication in the bloodstream,
becomes nonlinear if the fraction of medication used is a function of the concentration.
In the basic model, half is used no matter
row much there. More generally,
new concentration = old concentration − fraction used × old concentration + supplement.
Suppose the fraction used =. Write the discrete-time dynamical system and solve for the equilibrium.
第 5 題
In an excitable heart model. Let Vc be the threshold potential. The discrete-time dynamical system can be describe as
With the parameter values, compute the conditions on c for the existence of an equilibrium.
代入。若平衡電位 V 存在，它必滿足
若，則 且 。但是 c 是衰減係數，應小於 1，故不合。