Using this information: (a) Clearly identify your dependent and independent variables, in- cluding their units (b) Derive a differential equation for the rabbit population that takes all factors listed above into account, using the trick with h small and calculating the change
Using this information: (a) Clearly identify your dependent and independent variables, in- cluding their units (b) Derive a differential equation for the rabbit population that takes all factors listed above into account, using the trick with h small and calculating the change
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Our goal in this problem is to develop a model for the bunny population
by taking the following factors into account:
• The initial population on Jan 1 was 50 rabbits
On average, every rabbit has 0.1 offspring per month
On average, 30% of the existing rabbit population dies per
month
30 rabbits migrate into the
Using this information:
area per month.
(a) Clearly identify your dependent and independent variables, in-
cluding their units
(b) Derive a differential equation for the rabbit population that
takes all factors listed above into account, using the trick with h
small and calculating the change
(c) Perform a qualitative analysis: and the equilibrium solutions,
draw the bifurcation diagram, plot the equilibrium solution and
at least two other solutions, and determine if the equilibrium
solution is stable/unstable/bistable
(d) Solve the ODE, including the initial condition
(e) Use your solution to figure out what happens to the population
of bunnies as t→∞.
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