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Homework assignment 1
*
Due date: Wednesday September 12, 2007
1. Consider the population model again. Fix
f
= 1 and let
m
≥
0 be arbitrary.
(a) Show that the system is unstable and thus almost all solutions grow unbounded.
(b) Let’s modify the model to re±ect death of adults. Assume that all juveniles mature be
tween two consecutive censuses (so
f
= 1 in terms of our original model). Reproduction,
and right after that death, take place at the end of one cycle, right before the census
is taken. Only matures that were mature at the beginning of the cycle are capable of
reproduction. Thus, the juveniles that matured in this cycle don’t reproduce yet. Right
after reproduction some of the adults die and a fraction
s
survives to the census. This
census is the starting point of the next cycle. How does the original model change?
(Still assume that
m
≥
0 is arbitrary.) Give conditions for the parameters such that
the system is stable, asymptotically stable and unstable respectively. Show that the
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This note was uploaded on 09/12/2011 for the course MAP 4305 taught by Professor Deleenheer during the Summer '06 term at University of Florida.
 Summer '06
 DeLeenheer

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