Chapter 5 Flashcards
What is a dynamic equilibrium?
No net change in the system although individual rates are not equal to 0
What is a static equilibrium?
No change in the system; individual rates are equal to zero
What are two key system characteristics?
- Equilibria
- time coefficient
What does it mean when an equilibrium is stable?
It means after the system has a change it returns to the previous equilibrium.
When does a system have a stable equilibrium?
When it has negative feedback. This is because when a state has a value above the equilibrium the rates result negative while if it’s below the rates are positive. The rates decrease towards the equilibrium.
What happens when a system has a positive feedback?
A positive feedback has the opposite effect of a negative one. Systems tend to move away from their equilibria. ex. Exponential growth - when state is positive rates are positive and will increase with increasing rates.
What is the equation for time coefficient?
TC = |(S_equilibrium - S_t)/(dS/dt)|
or
TC = 1/”whatever is multiplied by the state”
works for both exponential and logistic systems
What is the time coefficient?
TC is the time needed for the model to reach its equilibrium state if the rate of change was fixed.
What is the average residence time?
ART is the average length of time that an entity will remain in a system.
What is the formula for ART in exponential growth?
ART = TC or = 1/c
What is the equation for an exponantial decay model?
A_t = A_0 * e^(-t/TC)
What is the equation for Euler’s scheme?
State _1+delta_t = state_t + delta_t * (dstate/dt)
What does the inverse of TC represent?
The inverse of TC (1/TC) represents the relative growth rate.
How can we estimate a good delta T for the model?
delta_t = TC / 10
What happens if delta_T is equal to TC?
The equilibrium is directly reached in 1 time step.
