Order of a system
Posted: Sat Sep 17, 2005 2:14 pm
Posted by Bill Braun <bbraun@hlthsys.com>
In Business Dynamics, p. 264, Sterman notes that, ""the order of a dynamic system or loop is the number of state variables, or stocks, it contains"". I've always understood this to exclude stocks that were simply sinks that accumulate activity over time but which did not make any dynamic contribution to the behavior of the model. (For example, in the classic first-order positive feedback loop model of a bank account, the interest that flows into the account balance stock could be summed into a separate stock that has no independent dynamic effect on the account balance.)
Is that understanding accurate?
In the SI model (pps. 301 & 302) he notes that, ""though the system has two stocks, it is actually a first order system because one of the stocks is completely determined by the other.""
Regarding the SIR model (p. 305) he notes, ""unlike the model considered thus far, the system is now second-order (there are three stocks, but since they sum to a constant, only two are independent).""
Could someone unpack the distinctions between these references? Thank you.
Bill Braun
Posted by Bill Braun <bbraun@hlthsys.com>
posting date Fri, 16 Sep 2005 07:39:24 -0500
In Business Dynamics, p. 264, Sterman notes that, ""the order of a dynamic system or loop is the number of state variables, or stocks, it contains"". I've always understood this to exclude stocks that were simply sinks that accumulate activity over time but which did not make any dynamic contribution to the behavior of the model. (For example, in the classic first-order positive feedback loop model of a bank account, the interest that flows into the account balance stock could be summed into a separate stock that has no independent dynamic effect on the account balance.)
Is that understanding accurate?
In the SI model (pps. 301 & 302) he notes that, ""though the system has two stocks, it is actually a first order system because one of the stocks is completely determined by the other.""
Regarding the SIR model (p. 305) he notes, ""unlike the model considered thus far, the system is now second-order (there are three stocks, but since they sum to a constant, only two are independent).""
Could someone unpack the distinctions between these references? Thank you.
Bill Braun
Posted by Bill Braun <bbraun@hlthsys.com>
posting date Fri, 16 Sep 2005 07:39:24 -0500