a. definition: stock stays at the same level because inflows = outflows
b. examples:
- streetcar
- bathtub with overflow
- container with a hole
- harvest rate
- predator-prey
- island biogeography for species
c. counter examples:
closed system - looking from the outside
equilibrium in a closed system is different than steady state the way we are using the term
zero flows in and out, might be considered steady state, but would be a trivial example or endpoint
a. number of people on the street car
at any one time, not total number of faces
people get on, people get off
during the middle of the run, it might be about even
it isn't that 15 people rode the whole distance
b. reservoir, such as a tub, has an overflow
water gets too high, flows off the top
sometimes it's important to follow the individuals or some sort of timing
marbles falling into a bowl
LI FO
stuffing mud into a pipe
LI LO
animals travelling through a corridor
conveyor belt with time of travel = 5 days for example
rain --> groundwater --> stream
creates a lag time
c. cylinder with outflow
rate of inflow causes volume to rise and the rate of outflow is matched
set up
start with a volume of 200 mL (cm^3) in a cylinder with radius = 10 cm
10 mL min^-1 inflow rate is fixed
outflow constant = 5 (mL min^-1)/cm of height
what is the steady state volume of the tub?
STELLA model (8-tub-flow)
example output
algebraic solution - on the board
EXCEL calculations (8-tub-flow.xls)
d. constant birth rate with increasing death rate as functions of the population
Stella model
e. Harvest rate
"logistic" growth equation
8-2-constant-harvest
set a particular harvest rate
try different rates
population adjusts to that rate
from above
not necessarily from below
"sensi-specs"
