1.4. What Is Dynamic Model ing?
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When a model is run on a computer, each element of the model is specified by initial conditions and the computer works out the system's responses according to the specified relations among elements. These initial
conditions may be based on measurement, such as the biomass of phytoplankton in the water column at a point in time and the number of otters
residing in a bay on a giving day, or estimates, such as estimates of the contact rate of infected manatee with uninfected ones. The estimates, in turn,
may be based on empirical information, or are just reasonable guesses by
the modeler and are used to illustrate the particular processes, rather than
provide exact empirical information.
Some of the elements that make up the system for which a model is
being developed are referred to as state variables. State variables mayor
may not be conserved. Each conserved state variable represents an accumulation or stock of materials or information. Typical conserved state variables are population, biomass, and heat energy . Nonconserved state variables are pure indicators of some aspects of the system's condition. A
typical nonconserved state variable is temperature.
System elements that represent the action or change in a state variable
are called flows or control variables. As a model is run over time, control
variables update the state variables at the end of each time step . Examples
for control variables are the number of births per month, a variable that
changes the state variable "population"; or investments per year changing
the state variable "number of boats ."
Typically, components of the system that is being modeled interact with
each other. Such interactions of system components are present in the form
of feedback processes. Feedback processes are said to occur if changes in
a system component initiate changes in other components that, in turn, affect the component that originally stimulated the change. Negative feedback exists if the change in a component leads to a response in other components that counteracts the original stimulus. For example, the increase in
the density of a prey species leads to an increase in predator density that,
in turn , reduces prey density. Analogously , positive feedback is present if
the change in a system component leads to changes in other components
that then strengthen the original process. For example, if there are unlimited resources, an increase in the number of births leads to an increase in
population size, which in turn causes the number of births to increase. Positive feedback can result in "explosive dynamics"-dynamics that lead a
system away from its original state . In the case of population dynamics , we
sometimes speak of population explosions.
Negative feedback processes tend to counteract a disturbance and lead
systems towards steady-state. One possible steady-state for interacting
predator and prey populations would be that the size of each population
stabilizes in the long run. Such stabilizing dynamics are in contrast to the
positive feedback processes that tend to amplify any disturbance, leading
systems away from equilibria.
11
When a model is run on a computer, each element of the model is specified by initial conditions and the computer works out the system's responses according to the specified relations among elements. These initial
conditions may be based on measurement, such as the biomass of phytoplankton in the water column at a point in time and the number of otters
residing in a bay on a giving day, or estimates, such as estimates of the contact rate of infected manatee with uninfected ones. The estimates, in turn,
may be based on empirical information, or are just reasonable guesses by
the modeler and are used to illustrate the particular processes, rather than
provide exact empirical information.
Some of the elements that make up the system for which a model is
being developed are referred to as state variables. State variables mayor
may not be conserved. Each conserved state variable represents an accumulation or stock of materials or information. Typical conserved state variables are population, biomass, and heat energy . Nonconserved state variables are pure indicators of some aspects of the system's condition. A
typical nonconserved state variable is temperature.
System elements that represent the action or change in a state variable
are called flows or control variables. As a model is run over time, control
variables update the state variables at the end of each time step . Examples
for control variables are the number of births per month, a variable that
changes the state variable "population"; or investments per year changing
the state variable "number of boats ."
Typically, components of the system that is being modeled interact with
each other. Such interactions of system components are present in the form
of feedback processes. Feedback processes are said to occur if changes in
a system component initiate changes in other components that, in turn, affect the component that originally stimulated the change. Negative feedback exists if the change in a component leads to a response in other components that counteracts the original stimulus. For example, the increase in
the density of a prey species leads to an increase in predator density that,
in turn , reduces prey density. Analogously , positive feedback is present if
the change in a system component leads to changes in other components
that then strengthen the original process. For example, if there are unlimited resources, an increase in the number of births leads to an increase in
population size, which in turn causes the number of births to increase. Positive feedback can result in "explosive dynamics"-dynamics that lead a
system away from its original state . In the case of population dynamics , we
sometimes speak of population explosions.
Negative feedback processes tend to counteract a disturbance and lead
systems towards steady-state. One possible steady-state for interacting
predator and prey populations would be that the size of each population
stabilizes in the long run. Such stabilizing dynamics are in contrast to the
positive feedback processes that tend to amplify any disturbance, leading
systems away from equilibria.