Chapter 5
Spatial Dynamics
There is no coming into being of aught that perishes, nor any end
for it. . . but only mingling, and separation of what has been
mingled.
(Empedocles)
5.1 Spatial Dynamics Model
In the previous chapters we have modeled population dynamics in response to
births and deaths, and we have assumed that the respective flows originate or
disappear in “clouds.” If we deal with migration in the context of population
dynamics we may want to explicitly model the source and recipients of the flows
of migrants. This is the topic of this chapter. The model developed here is quite
general and provides a basis for our discussion of spatial dynamics in later chapters.
Here is what might be called a “mobility framework,” where migration from one
state to another depends only on the current status of the donor state. Mobility might
be the movement of animals between various resource points, chemical diffusion,
the circulation of money, or the location of people in towns on a landscape.
Mobility is defined by flows that are calculated as the difference between the
value of the state variables at two points on the landscape. This difference is then
multiplied by a fixed coefficient that reflects the strength of migration. The
STELLA model is shown in Fig. 5.1.
Figure 5.2 shows the egalitarian or the strict diffusion solution—no matter what
the initial status of each of the states, all stocks find the same equilibrium. This is
due to the fact that each of the exchanges is multiplied by the same coefficient.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_5,
© Springer International Publishing Switzerland 2014
59
Spatial Dynamics
There is no coming into being of aught that perishes, nor any end
for it. . . but only mingling, and separation of what has been
mingled.
(Empedocles)
5.1 Spatial Dynamics Model
In the previous chapters we have modeled population dynamics in response to
births and deaths, and we have assumed that the respective flows originate or
disappear in “clouds.” If we deal with migration in the context of population
dynamics we may want to explicitly model the source and recipients of the flows
of migrants. This is the topic of this chapter. The model developed here is quite
general and provides a basis for our discussion of spatial dynamics in later chapters.
Here is what might be called a “mobility framework,” where migration from one
state to another depends only on the current status of the donor state. Mobility might
be the movement of animals between various resource points, chemical diffusion,
the circulation of money, or the location of people in towns on a landscape.
Mobility is defined by flows that are calculated as the difference between the
value of the state variables at two points on the landscape. This difference is then
multiplied by a fixed coefficient that reflects the strength of migration. The
STELLA model is shown in Fig. 5.1.
Figure 5.2 shows the egalitarian or the strict diffusion solution—no matter what
the initial status of each of the states, all stocks find the same equilibrium. This is
due to the fact that each of the exchanges is multiplied by the same coefficient.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_5,
© Springer International Publishing Switzerland 2014
59