# 
msgid ""
msgstr ""
"Project-Id-Version: Modelica by Example v0.3.6\n"
"Report-Msgid-Bugs-To: \n"
"POT-Creation-Date: 2015-09-29 16:40-0400\n"
"PO-Revision-Date: YEAR-MO-DA HO:MI+ZONE\n"
"Last-Translator: FULL NAME <EMAIL@ADDRESS>\n"
"Language-Team: LANGUAGE <LL@li.org>\n"
"MIME-Version: 1.0\n"
"Content-Type: text/plain; charset=UTF-8\n"
"Content-Transfer-Encoding: 8bit\n"

#: ../../source/components/subsystems/population.rst:2
msgid "Lotka-Volterra with Migration"
msgstr ""

#: ../../source/components/subsystems/population.rst:4
msgid ""
"In this section, we will once again revisit the Lotka-Volterra models to "
"understand how we can build on the work we've already done of creating "
"reusable component models.  We will now take the next step and create "
"reusable models of individual geographical regions (each with the usual "
"population dynamics) and then connect those geographical regions together "
"with migration models."
msgstr ""

#: ../../source/components/subsystems/population.rst:12
msgid "Two Species Region"
msgstr ""

#: ../../source/components/subsystems/population.rst:14
msgid ""
"The models in this section will all make use of the following model that "
"represents a region consisting of two populations, one of rabbits and the "
"other foxes, with the usual Lotka-Volterra population dynamics.  The "
"Modelica source code for the model is:"
msgstr ""

#: ../../source/components/subsystems/population.rst:23
msgid "The diagram for this component is rendered as:"
msgstr ""

#: ../../source/components/subsystems/population.rst:30
msgid ""
"This model will be used as the basis for the regional population dynamics in"
" subsequent models presented in this section."
msgstr ""

#: ../../source/components/subsystems/population.rst:34
msgid "Unconnected Regions"
msgstr ""

#: ../../source/components/subsystems/population.rst:36
msgid ""
"We'll start by building a model that consists of four unconnected regions.  "
"The Modelica source code for such a model is quite simple:"
msgstr ""

#: ../../source/components/subsystems/population.rst:42
msgid "The diagram for this model is equally simple:"
msgstr ""

#: ../../source/components/subsystems/population.rst:49
msgid ""
"If we simulate this model, each population should follow the same trajectory"
" since their initial conditions are identical.  The following plot shows "
"that this is, in fact, the case:"
msgstr ""

#: ../../source/components/subsystems/population.rst:56
msgid ""
"In a moment, we'll look at the effects of migration.  But in order to fully "
"appreciate the effect that migration has, we'll need to introduce some "
"differences in the evolution of the different regions. So let's modify the "
"initial conditions of the ``UnconnectedPopulations`` model to introduce some"
" regional variation:"
msgstr ""

#: ../../source/components/subsystems/population.rst:65
msgid ""
"Simulating this model, we see that each region has a slightly different "
"population dynamic:"
msgstr ""

#: ../../source/components/subsystems/population.rst:72
msgid "Migration"
msgstr ""

#: ../../source/components/subsystems/population.rst:74
msgid ""
"Now that we have simulated the population dynamics in four **unconnected** "
"regions, it would be interesting to note the impact that migration might "
"have on these dynamics."
msgstr ""

#: ../../source/components/subsystems/population.rst:78
msgid "Consider the following Modelica model for migration:"
msgstr ""

#: ../../source/components/subsystems/population.rst:83
msgid ""
"This model looks at the population of both rabbits and foxes in the "
"connected regions and specifies a rate of migration that is proportional to "
"the difference in population between the regions.  In other words, if there "
"are more rabbits in one region than another, the rabbits will move from the "
"more populated region to the less population region.  This is effectively a "
"\"diffusion\" model of migration and does not necessarily have a basis in "
"ecology.  It is introduced simply as an example of how we could add "
"additional effects, on top of those implemented in each region, to change "
"the population dynamics between regions."
msgstr ""

#: ../../source/components/subsystems/population.rst:94
msgid ""
"If we connect our previously unconnected regions with migration paths, "
"*e.g.,*"
msgstr ""

#: ../../source/components/subsystems/population.rst:100
msgid "the resulting system diagram becomes:"
msgstr ""

#: ../../source/components/subsystems/population.rst:107
msgid ""
"Simulating this system, we see that the population dynamics in the different"
" regions start off out of sync, but eventually stabilize into repeating "
"patterns:"
msgstr ""

#: ../../source/components/subsystems/population.rst:115
msgid "Conclusion"
msgstr ""

#: ../../source/components/subsystems/population.rst:117
msgid ""
"Earlier, we turned the Lotka-Volterra equations into components representing"
" predation, starvation and reproduction.  In this section, we were able to "
"use those component models to build up subsystem models to represent the "
"population dynamics in a particular region and then link those subsystems "
"together into a hierarchical system model that also captured the effects of "
"migration between these distinct regions."
msgstr ""
